Date: 2016-07-24T17:16:04+00:00

Actual source code: morethuente.c
petsc-3.7.3 2016-07-24
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      1: #include <petsc/private/taolinesearchimpl.h>
      2: #include <../src/tao/linesearch/impls/morethuente/morethuente.h>

      4: /*
      5:    This algorithm is taken from More' and Thuente, "Line search algorithms
      6:    with guaranteed sufficient decrease", Argonne National Laboratory,
      7:    Technical Report MCS-P330-1092.
      8: */

     10: static PetscErrorCode Tao_mcstep(TaoLineSearch ls,PetscReal *stx,PetscReal *fx,PetscReal *dx,PetscReal *sty,PetscReal *fy,PetscReal *dy,PetscReal *stp,PetscReal *fp,PetscReal *dp);

     14: static PetscErrorCode TaoLineSearchDestroy_MT(TaoLineSearch ls)
     15: {
     16:   PetscErrorCode   ierr;
     17:   TaoLineSearch_MT *mt;

     21:   mt = (TaoLineSearch_MT*)(ls->data);
     22:   if (mt->x) {
     23:     PetscObjectDereference((PetscObject)mt->x);
     24:   }
     25:   VecDestroy(&mt->work);
     26:   PetscFree(ls->data);
     27:   return(0);
     28: }

     32: static PetscErrorCode TaoLineSearchSetFromOptions_MT(PetscOptionItems *PetscOptionsObject,TaoLineSearch ls)
     33: {
     36:   return(0);
     37: }

     42: /* @ TaoApply_LineSearch - This routine takes step length of 1.0.

     44:    Input Parameters:
     45: +  tao - Tao context
     46: .  X - current iterate (on output X contains new iterate, X + step*S)
     47: .  f - objective function evaluated at X
     48: .  G - gradient evaluated at X
     49: -  D - search direction

     52:    Info is set to 0.

     54: @ */

     56: static PetscErrorCode TaoLineSearchApply_MT(TaoLineSearch ls, Vec x, PetscReal *f, Vec g, Vec s)
     57: {
     58:   PetscErrorCode   ierr;
     59:   TaoLineSearch_MT *mt;

     61:   PetscReal        xtrapf = 4.0;
     62:   PetscReal        finit, width, width1, dginit, fm, fxm, fym, dgm, dgxm, dgym;
     63:   PetscReal        dgx, dgy, dg, dg2, fx, fy, stx, sty, dgtest;
     64:   PetscReal        ftest1=0.0, ftest2=0.0;
     65:   PetscInt         i, stage1,n1,n2,nn1,nn2;
     66:   PetscReal        bstepmin1, bstepmin2, bstepmax;
     67:   PetscBool        g_computed=PETSC_FALSE; /* to prevent extra gradient computation */

     76:   /* comm,type,size checks are done in interface TaoLineSearchApply */
     77:   mt = (TaoLineSearch_MT*)(ls->data);
     78:   ls->reason = TAOLINESEARCH_CONTINUE_ITERATING;

     80:   /* Check work vector */
     81:   if (!mt->work) {
     82:     VecDuplicate(x,&mt->work);
     83:     mt->x = x;
     84:     PetscObjectReference((PetscObject)mt->x);
     85:   } else if (x != mt->x) {
     86:     VecDestroy(&mt->work);
     87:     VecDuplicate(x,&mt->work);
     88:     PetscObjectDereference((PetscObject)mt->x);
     89:     mt->x = x;
     90:     PetscObjectReference((PetscObject)mt->x);
     91:   }

     93:   if (ls->bounded) {
     94:     /* Compute step length needed to make all variables equal a bound */
     95:     /* Compute the smallest steplength that will make one nonbinding variable
     96:      equal the bound */
     97:     VecGetLocalSize(ls->upper,&n1);
     98:     VecGetLocalSize(mt->x, &n2);
     99:     VecGetSize(ls->upper,&nn1);
    100:     VecGetSize(mt->x,&nn2);
    101:     if (n1 != n2 || nn1 != nn2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Variable vector not compatible with bounds vector");
    102:     VecScale(s,-1.0);
    103:     VecBoundGradientProjection(s,x,ls->lower,ls->upper,s);
    104:     VecScale(s,-1.0);
    105:     VecStepBoundInfo(x,s,ls->lower,ls->upper,&bstepmin1,&bstepmin2,&bstepmax);
    106:     ls->stepmax = PetscMin(bstepmax,1.0e15);
    107:   }

    109:   VecDot(g,s,&dginit);
    110:   if (PetscIsInfOrNanReal(dginit)) {
    111:     PetscInfo1(ls,"Initial Line Search step * g is Inf or Nan (%g)\n",(double)dginit);
    112:     ls->reason=TAOLINESEARCH_FAILED_INFORNAN;
    113:     return(0);
    114:   }
    115:   if (dginit >= 0.0) {
    116:     PetscInfo1(ls,"Initial Line Search step * g is not descent direction (%g)\n",(double)dginit);
    117:     ls->reason = TAOLINESEARCH_FAILED_ASCENT;
    118:     return(0);
    119:   }

    122:   /* Initialization */
    123:   mt->bracket = 0;
    124:   stage1 = 1;
    125:   finit = *f;
    126:   dgtest = ls->ftol * dginit;
    127:   width = ls->stepmax - ls->stepmin;
    128:   width1 = width * 2.0;
    129:   VecCopy(x,mt->work);
    130:   /* Variable dictionary:
    131:    stx, fx, dgx - the step, function, and derivative at the best step
    132:    sty, fy, dgy - the step, function, and derivative at the other endpoint
    133:    of the interval of uncertainty
    134:    step, f, dg - the step, function, and derivative at the current step */

    136:   stx = 0.0;
    137:   fx  = finit;
    138:   dgx = dginit;
    139:   sty = 0.0;
    140:   fy  = finit;
    141:   dgy = dginit;

    143:   ls->step=ls->initstep;
    144:   for (i=0; i< ls->max_funcs; i++) {
    145:     /* Set min and max steps to correspond to the interval of uncertainty */
    146:     if (mt->bracket) {
    147:       ls->stepmin = PetscMin(stx,sty);
    148:       ls->stepmax = PetscMax(stx,sty);
    149:     } else {
    150:       ls->stepmin = stx;
    151:       ls->stepmax = ls->step + xtrapf * (ls->step - stx);
    152:     }

    154:     /* Force the step to be within the bounds */
    155:     ls->step = PetscMax(ls->step,ls->stepmin);
    156:     ls->step = PetscMin(ls->step,ls->stepmax);

    158:     /* If an unusual termination is to occur, then let step be the lowest
    159:      point obtained thus far */
    160:     if ((stx!=0) && (((mt->bracket) && (ls->step <= ls->stepmin || ls->step >= ls->stepmax)) || ((mt->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol * ls->stepmax)) ||
    161:                      ((ls->nfeval+ls->nfgeval) >= ls->max_funcs - 1) || (mt->infoc == 0))) {
    162:       ls->step = stx;
    163:     }

    165:     VecCopy(x,mt->work);
    166:     VecAXPY(mt->work,ls->step,s);   /* W = X + step*S */

    168:     if (ls->bounded) {
    169:       VecMedian(ls->lower, mt->work, ls->upper, mt->work);
    170:     }
    171:     if (ls->usegts) {
    172:       TaoLineSearchComputeObjectiveAndGTS(ls,mt->work,f,&dg);
    173:       g_computed=PETSC_FALSE;
    174:     } else {
    175:       TaoLineSearchComputeObjectiveAndGradient(ls,mt->work,f,g);
    176:       g_computed=PETSC_TRUE;
    177:       if (ls->bounded) {
    178:         VecDot(g,x,&dg);
    179:         VecDot(g,mt->work,&dg2);
    180:         dg = (dg2 - dg)/ls->step;
    181:       } else {
    182:         VecDot(g,s,&dg);
    183:       }
    184:     }

    186:     if (0 == i) {
    187:       ls->f_fullstep=*f;
    188:     }

    190:     if (PetscIsInfOrNanReal(*f) || PetscIsInfOrNanReal(dg)) {
    191:       /* User provided compute function generated Not-a-Number, assume
    192:        domain violation and set function value and directional
    193:        derivative to infinity. */
    194:       *f = PETSC_INFINITY;
    195:       dg = PETSC_INFINITY;
    196:     }

    198:     ftest1 = finit + ls->step * dgtest;
    199:     if (ls->bounded) {
    200:       ftest2 = finit + ls->step * dgtest * ls->ftol;
    201:     }
    202:     /* Convergence testing */
    203:     if (((*f - ftest1 <= 1.0e-10 * PetscAbsReal(finit)) &&  (PetscAbsReal(dg) + ls->gtol*dginit <= 0.0))) {
    204:       PetscInfo(ls, "Line search success: Sufficient decrease and directional deriv conditions hold\n");
    205:       ls->reason = TAOLINESEARCH_SUCCESS;
    206:       break;
    207:     }

    209:     /* Check Armijo if beyond the first breakpoint */
    210:     if (ls->bounded && (*f <= ftest2) && (ls->step >= bstepmin2)) {
    211:       PetscInfo(ls,"Line search success: Sufficient decrease.\n");
    212:       ls->reason = TAOLINESEARCH_SUCCESS;
    213:       break;
    214:     }

    216:     /* Checks for bad cases */
    217:     if (((mt->bracket) && (ls->step <= ls->stepmin||ls->step >= ls->stepmax)) || (!mt->infoc)) {
    218:       PetscInfo(ls,"Rounding errors may prevent further progress.  May not be a step satisfying\n");
    219:       PetscInfo(ls,"sufficient decrease and curvature conditions. Tolerances may be too small.\n");
    220:       ls->reason = TAOLINESEARCH_HALTED_OTHER;
    221:       break;
    222:     }
    223:     if ((ls->step == ls->stepmax) && (*f <= ftest1) && (dg <= dgtest)) {
    224:       PetscInfo1(ls,"Step is at the upper bound, stepmax (%g)\n",(double)ls->stepmax);
    225:       ls->reason = TAOLINESEARCH_HALTED_UPPERBOUND;
    226:       break;
    227:     }
    228:     if ((ls->step == ls->stepmin) && (*f >= ftest1) && (dg >= dgtest)) {
    229:       PetscInfo1(ls,"Step is at the lower bound, stepmin (%g)\n",(double)ls->stepmin);
    230:       ls->reason = TAOLINESEARCH_HALTED_LOWERBOUND;
    231:       break;
    232:     }
    233:     if ((mt->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol*ls->stepmax)){
    234:       PetscInfo1(ls,"Relative width of interval of uncertainty is at most rtol (%g)\n",(double)ls->rtol);
    235:       ls->reason = TAOLINESEARCH_HALTED_RTOL;
    236:       break;
    237:     }

    239:     /* In the first stage, we seek a step for which the modified function
    240:      has a nonpositive value and nonnegative derivative */
    241:     if ((stage1) && (*f <= ftest1) && (dg >= dginit * PetscMin(ls->ftol, ls->gtol))) {
    242:       stage1 = 0;
    243:     }

    245:     /* A modified function is used to predict the step only if we
    246:      have not obtained a step for which the modified function has a
    247:      nonpositive function value and nonnegative derivative, and if a
    248:      lower function value has been obtained but the decrease is not
    249:      sufficient */

    251:     if ((stage1) && (*f <= fx) && (*f > ftest1)) {
    252:       fm   = *f - ls->step * dgtest;    /* Define modified function */
    253:       fxm  = fx - stx * dgtest;         /* and derivatives */
    254:       fym  = fy - sty * dgtest;
    255:       dgm  = dg - dgtest;
    256:       dgxm = dgx - dgtest;
    257:       dgym = dgy - dgtest;

    259:       /* if (dgxm * (ls->step - stx) >= 0.0) */
    260:       /* Update the interval of uncertainty and compute the new step */
    261:       Tao_mcstep(ls,&stx,&fxm,&dgxm,&sty,&fym,&dgym,&ls->step,&fm,&dgm);

    263:       fx  = fxm + stx * dgtest; /* Reset the function and */
    264:       fy  = fym + sty * dgtest; /* gradient values */
    265:       dgx = dgxm + dgtest;
    266:       dgy = dgym + dgtest;
    267:     } else {
    268:       /* Update the interval of uncertainty and compute the new step */
    269:       Tao_mcstep(ls,&stx,&fx,&dgx,&sty,&fy,&dgy,&ls->step,f,&dg);
    270:     }

    272:     /* Force a sufficient decrease in the interval of uncertainty */
    273:     if (mt->bracket) {
    274:       if (PetscAbsReal(sty - stx) >= 0.66 * width1) ls->step = stx + 0.5*(sty - stx);
    275:       width1 = width;
    276:       width = PetscAbsReal(sty - stx);
    277:     }
    278:   }
    279:   if ((ls->nfeval+ls->nfgeval) > ls->max_funcs) {
    280:     PetscInfo2(ls,"Number of line search function evals (%D) > maximum (%D)\n",(ls->nfeval+ls->nfgeval),ls->max_funcs);
    281:     ls->reason = TAOLINESEARCH_HALTED_MAXFCN;
    282:   }

    284:   /* Finish computations */
    285:   PetscInfo2(ls,"%D function evals in line search, step = %g\n",(ls->nfeval+ls->nfgeval),(double)ls->step);

    287:   /* Set new solution vector and compute gradient if needed */
    288:   VecCopy(mt->work,x);
    289:   if (!g_computed) {
    290:     TaoLineSearchComputeGradient(ls,mt->work,g);
    291:   }
    292:   return(0);
    293: }

    297: PETSC_EXTERN PetscErrorCode TaoLineSearchCreate_MT(TaoLineSearch ls)
    298: {
    299:   PetscErrorCode   ierr;
    300:   TaoLineSearch_MT *ctx;

    304:   PetscNewLog(ls,&ctx);
    305:   ctx->bracket=0;
    306:   ctx->infoc=1;
    307:   ls->data = (void*)ctx;
    308:   ls->initstep = 1.0;
    309:   ls->ops->setup=0;
    310:   ls->ops->reset=0;
    311:   ls->ops->apply=TaoLineSearchApply_MT;
    312:   ls->ops->destroy=TaoLineSearchDestroy_MT;
    313:   ls->ops->setfromoptions=TaoLineSearchSetFromOptions_MT;
    314:   return(0);
    315: }

    317: /*
    318:      The subroutine mcstep is taken from the work of Jorge Nocedal.
    319:      this is a variant of More' and Thuente's routine.

    321:      subroutine mcstep

    323:      the purpose of mcstep is to compute a safeguarded step for
    324:      a linesearch and to update an interval of uncertainty for
    325:      a minimizer of the function.

    327:      the parameter stx contains the step with the least function
    328:      value. the parameter stp contains the current step. it is
    329:      assumed that the derivative at stx is negative in the
    330:      direction of the step. if bracket is set true then a
    331:      minimizer has been bracketed in an interval of uncertainty
    332:      with endpoints stx and sty.

    334:      the subroutine statement is

    336:      subroutine mcstep(stx,fx,dx,sty,fy,dy,stp,fp,dp,bracket,
    337:                        stpmin,stpmax,info)

    339:      where

    341:        stx, fx, and dx are variables which specify the step,
    342:          the function, and the derivative at the best step obtained
    343:          so far. The derivative must be negative in the direction
    344:          of the step, that is, dx and stp-stx must have opposite
    345:          signs. On output these parameters are updated appropriately.

    347:        sty, fy, and dy are variables which specify the step,
    348:          the function, and the derivative at the other endpoint of
    349:          the interval of uncertainty. On output these parameters are
    350:          updated appropriately.

    352:        stp, fp, and dp are variables which specify the step,
    353:          the function, and the derivative at the current step.
    354:          If bracket is set true then on input stp must be
    355:          between stx and sty. On output stp is set to the new step.

    357:        bracket is a logical variable which specifies if a minimizer
    358:          has been bracketed.  If the minimizer has not been bracketed
    359:          then on input bracket must be set false.  If the minimizer
    360:          is bracketed then on output bracket is set true.

    362:        stpmin and stpmax are input variables which specify lower
    363:          and upper bounds for the step.

    365:        info is an integer output variable set as follows:
    366:          if info = 1,2,3,4,5, then the step has been computed
    367:          according to one of the five cases below. otherwise
    368:          info = 0, and this indicates improper input parameters.

    370:      subprograms called

    372:        fortran-supplied ... abs,max,min,sqrt

    374:      argonne national laboratory. minpack project. june 1983
    375:      jorge j. more', david j. thuente

    377: */

    381: static PetscErrorCode Tao_mcstep(TaoLineSearch ls,PetscReal *stx,PetscReal *fx,PetscReal *dx,PetscReal *sty,PetscReal *fy,PetscReal *dy,PetscReal *stp,PetscReal *fp,PetscReal *dp)
    382: {
    383:   TaoLineSearch_MT *mtP = (TaoLineSearch_MT *) ls->data;
    384:   PetscReal        gamma1, p, q, r, s, sgnd, stpc, stpf, stpq, theta;
    385:   PetscInt         bound;

    388:   /* Check the input parameters for errors */
    389:   mtP->infoc = 0;
    390:   if (mtP->bracket && (*stp <= PetscMin(*stx,*sty) || (*stp >= PetscMax(*stx,*sty)))) SETERRQ(PETSC_COMM_SELF,1,"bad stp in bracket");
    391:   if (*dx * (*stp-*stx) >= 0.0) SETERRQ(PETSC_COMM_SELF,1,"dx * (stp-stx) >= 0.0");
    392:   if (ls->stepmax < ls->stepmin) SETERRQ(PETSC_COMM_SELF,1,"stepmax > stepmin");

    394:   /* Determine if the derivatives have opposite sign */
    395:   sgnd = *dp * (*dx / PetscAbsReal(*dx));

    397:   if (*fp > *fx) {
    398:     /* Case 1: a higher function value.
    399:      The minimum is bracketed. If the cubic step is closer
    400:      to stx than the quadratic step, the cubic step is taken,
    401:      else the average of the cubic and quadratic steps is taken. */

    403:     mtP->infoc = 1;
    404:     bound = 1;
    405:     theta = 3 * (*fx - *fp) / (*stp - *stx) + *dx + *dp;
    406:     s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dx));
    407:     s = PetscMax(s,PetscAbsReal(*dp));
    408:     gamma1 = s*PetscSqrtScalar(PetscPowScalar(theta/s,2.0) - (*dx/s)*(*dp/s));
    409:     if (*stp < *stx) gamma1 = -gamma1;
    410:     /* Can p be 0?  Check */
    411:     p = (gamma1 - *dx) + theta;
    412:     q = ((gamma1 - *dx) + gamma1) + *dp;
    413:     r = p/q;
    414:     stpc = *stx + r*(*stp - *stx);
    415:     stpq = *stx + ((*dx/((*fx-*fp)/(*stp-*stx)+*dx))*0.5) * (*stp - *stx);

    417:     if (PetscAbsReal(stpc-*stx) < PetscAbsReal(stpq-*stx)) {
    418:       stpf = stpc;
    419:     } else {
    420:       stpf = stpc + 0.5*(stpq - stpc);
    421:     }
    422:     mtP->bracket = 1;
    423:   } else if (sgnd < 0.0) {
    424:     /* Case 2: A lower function value and derivatives of
    425:      opposite sign. The minimum is bracketed. If the cubic
    426:      step is closer to stx than the quadratic (secant) step,
    427:      the cubic step is taken, else the quadratic step is taken. */

    429:     mtP->infoc = 2;
    430:     bound = 0;
    431:     theta = 3*(*fx - *fp)/(*stp - *stx) + *dx + *dp;
    432:     s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dx));
    433:     s = PetscMax(s,PetscAbsReal(*dp));
    434:     gamma1 = s*PetscSqrtScalar(PetscPowScalar(theta/s,2.0) - (*dx/s)*(*dp/s));
    435:     if (*stp > *stx) gamma1 = -gamma1;
    436:     p = (gamma1 - *dp) + theta;
    437:     q = ((gamma1 - *dp) + gamma1) + *dx;
    438:     r = p/q;
    439:     stpc = *stp + r*(*stx - *stp);
    440:     stpq = *stp + (*dp/(*dp-*dx))*(*stx - *stp);

    442:     if (PetscAbsReal(stpc-*stp) > PetscAbsReal(stpq-*stp)) {
    443:       stpf = stpc;
    444:     } else {
    445:       stpf = stpq;
    446:     }
    447:     mtP->bracket = 1;
    448:   } else if (PetscAbsReal(*dp) < PetscAbsReal(*dx)) {
    449:     /* Case 3: A lower function value, derivatives of the
    450:      same sign, and the magnitude of the derivative decreases.
    451:      The cubic step is only used if the cubic tends to infinity
    452:      in the direction of the step or if the minimum of the cubic
    453:      is beyond stp. Otherwise the cubic step is defined to be
    454:      either stepmin or stepmax. The quadratic (secant) step is also
    455:      computed and if the minimum is bracketed then the step
    456:      closest to stx is taken, else the step farthest away is taken. */

    458:     mtP->infoc = 3;
    459:     bound = 1;
    460:     theta = 3*(*fx - *fp)/(*stp - *stx) + *dx + *dp;
    461:     s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dx));
    462:     s = PetscMax(s,PetscAbsReal(*dp));

    464:     /* The case gamma1 = 0 only arises if the cubic does not tend
    465:        to infinity in the direction of the step. */
    466:     gamma1 = s*PetscSqrtScalar(PetscMax(0.0,PetscPowScalar(theta/s,2.0) - (*dx/s)*(*dp/s)));
    467:     if (*stp > *stx) gamma1 = -gamma1;
    468:     p = (gamma1 - *dp) + theta;
    469:     q = (gamma1 + (*dx - *dp)) + gamma1;
    470:     r = p/q;
    471:     if (r < 0.0 && gamma1 != 0.0) stpc = *stp + r*(*stx - *stp);
    472:     else if (*stp > *stx)        stpc = ls->stepmax;
    473:     else                         stpc = ls->stepmin;
    474:     stpq = *stp + (*dp/(*dp-*dx)) * (*stx - *stp);

    476:     if (mtP->bracket) {
    477:       if (PetscAbsReal(*stp-stpc) < PetscAbsReal(*stp-stpq)) {
    478:         stpf = stpc;
    479:       } else {
    480:         stpf = stpq;
    481:       }
    482:     } else {
    483:       if (PetscAbsReal(*stp-stpc) > PetscAbsReal(*stp-stpq)) {
    484:         stpf = stpc;
    485:       } else {
    486:         stpf = stpq;
    487:       }
    488:     }
    489:   } else {
    490:     /* Case 4: A lower function value, derivatives of the
    491:        same sign, and the magnitude of the derivative does
    492:        not decrease. If the minimum is not bracketed, the step
    493:        is either stpmin or stpmax, else the cubic step is taken. */

    495:     mtP->infoc = 4;
    496:     bound = 0;
    497:     if (mtP->bracket) {
    498:       theta = 3*(*fp - *fy)/(*sty - *stp) + *dy + *dp;
    499:       s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dy));
    500:       s = PetscMax(s,PetscAbsReal(*dp));
    501:       gamma1 = s*PetscSqrtScalar(PetscPowScalar(theta/s,2.0) - (*dy/s)*(*dp/s));
    502:       if (*stp > *sty) gamma1 = -gamma1;
    503:       p = (gamma1 - *dp) + theta;
    504:       q = ((gamma1 - *dp) + gamma1) + *dy;
    505:       r = p/q;
    506:       stpc = *stp + r*(*sty - *stp);
    507:       stpf = stpc;
    508:     } else if (*stp > *stx) {
    509:       stpf = ls->stepmax;
    510:     } else {
    511:       stpf = ls->stepmin;
    512:     }
    513:   }

    515:   /* Update the interval of uncertainty.  This update does not
    516:      depend on the new step or the case analysis above. */

    518:   if (*fp > *fx) {
    519:     *sty = *stp;
    520:     *fy = *fp;
    521:     *dy = *dp;
    522:   } else {
    523:     if (sgnd < 0.0) {
    524:       *sty = *stx;
    525:       *fy = *fx;
    526:       *dy = *dx;
    527:     }
    528:     *stx = *stp;
    529:     *fx = *fp;
    530:     *dx = *dp;
    531:   }

    533:   /* Compute the new step and safeguard it. */
    534:   stpf = PetscMin(ls->stepmax,stpf);
    535:   stpf = PetscMax(ls->stepmin,stpf);
    536:   *stp = stpf;
    537:   if (mtP->bracket && bound) {
    538:     if (*sty > *stx) {
    539:       *stp = PetscMin(*stx+0.66*(*sty-*stx),*stp);
    540:     } else {
    541:       *stp = PetscMax(*stx+0.66*(*sty-*stx),*stp);
    542:     }
    543:   }
    544:   return(0);
    545: }