Date: 2015-10-02T22:31:06+00:00

Actual source code: morethuente.c
petsc-3.6.2 2015-10-02
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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(PetscOptions *PetscOptionsObject,TaoLineSearch ls)
     33: {
     36:   return(0);
     37: }

     41: static PetscErrorCode TaoLineSearchView_MT(TaoLineSearch ls, PetscViewer pv)
     42: {
     44:   PetscBool      isascii;

     47:   PetscObjectTypeCompare((PetscObject)pv, PETSCVIEWERASCII, &isascii);
     48:   if (isascii) {
     49:     PetscViewerASCIIPrintf(pv,"  maxf=%D, ftol=%g, gtol=%g\n",ls->max_funcs,(double)ls->rtol,(double)ls->ftol);
     50:   }
     51:   return(0);
     52: }

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

     58:    Input Parameters:
     59: +  tao - Tao context
     60: .  X - current iterate (on output X contains new iterate, X + step*S)
     61: .  f - objective function evaluated at X
     62: .  G - gradient evaluated at X
     63: -  D - search direction

     66:    Info is set to 0.

     68: @ */

     70: static PetscErrorCode TaoLineSearchApply_MT(TaoLineSearch ls, Vec x, PetscReal *f, Vec g, Vec s)
     71: {
     72:   PetscErrorCode   ierr;
     73:   TaoLineSearch_MT *mt;

     75:   PetscReal        xtrapf = 4.0;
     76:   PetscReal        finit, width, width1, dginit, fm, fxm, fym, dgm, dgxm, dgym;
     77:   PetscReal        dgx, dgy, dg, dg2, fx, fy, stx, sty, dgtest;
     78:   PetscReal        ftest1=0.0, ftest2=0.0;
     79:   PetscInt         i, stage1,n1,n2,nn1,nn2;
     80:   PetscReal        bstepmin1, bstepmin2, bstepmax;
     81:   PetscBool        g_computed=PETSC_FALSE; /* to prevent extra gradient computation */

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

     94:   /* Check work vector */
     95:   if (!mt->work) {
     96:     VecDuplicate(x,&mt->work);
     97:     mt->x = x;
     98:     PetscObjectReference((PetscObject)mt->x);
     99:   } else if (x != mt->x) {
    100:     VecDestroy(&mt->work);
    101:     VecDuplicate(x,&mt->work);
    102:     PetscObjectDereference((PetscObject)mt->x);
    103:     mt->x = x;
    104:     PetscObjectReference((PetscObject)mt->x);
    105:   }

    107:   if (ls->bounded) {
    108:     /* Compute step length needed to make all variables equal a bound */
    109:     /* Compute the smallest steplength that will make one nonbinding variable
    110:      equal the bound */
    111:     VecGetLocalSize(ls->upper,&n1);
    112:     VecGetLocalSize(mt->x, &n2);
    113:     VecGetSize(ls->upper,&nn1);
    114:     VecGetSize(mt->x,&nn2);
    115:     if (n1 != n2 || nn1 != nn2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Variable vector not compatible with bounds vector");
    116:     VecScale(s,-1.0);
    117:     VecBoundGradientProjection(s,x,ls->lower,ls->upper,s);
    118:     VecScale(s,-1.0);
    119:     VecStepBoundInfo(x,s,ls->lower,ls->upper,&bstepmin1,&bstepmin2,&bstepmax);
    120:     ls->stepmax = PetscMin(bstepmax,1.0e15);
    121:   }

    123:   VecDot(g,s,&dginit);
    124:   if (PetscIsInfOrNanReal(dginit)) {
    125:     PetscInfo1(ls,"Initial Line Search step * g is Inf or Nan (%g)\n",(double)dginit);
    126:     ls->reason=TAOLINESEARCH_FAILED_INFORNAN;
    127:     return(0);
    128:   }
    129:   if (dginit >= 0.0) {
    130:     PetscInfo1(ls,"Initial Line Search step * g is not descent direction (%g)\n",(double)dginit);
    131:     ls->reason = TAOLINESEARCH_FAILED_ASCENT;
    132:     return(0);
    133:   }

    136:   /* Initialization */
    137:   mt->bracket = 0;
    138:   stage1 = 1;
    139:   finit = *f;
    140:   dgtest = ls->ftol * dginit;
    141:   width = ls->stepmax - ls->stepmin;
    142:   width1 = width * 2.0;
    143:   VecCopy(x,mt->work);
    144:   /* Variable dictionary:
    145:    stx, fx, dgx - the step, function, and derivative at the best step
    146:    sty, fy, dgy - the step, function, and derivative at the other endpoint
    147:    of the interval of uncertainty
    148:    step, f, dg - the step, function, and derivative at the current step */

    150:   stx = 0.0;
    151:   fx  = finit;
    152:   dgx = dginit;
    153:   sty = 0.0;
    154:   fy  = finit;
    155:   dgy = dginit;

    157:   ls->step=ls->initstep;
    158:   for (i=0; i< ls->max_funcs; i++) {
    159:     /* Set min and max steps to correspond to the interval of uncertainty */
    160:     if (mt->bracket) {
    161:       ls->stepmin = PetscMin(stx,sty);
    162:       ls->stepmax = PetscMax(stx,sty);
    163:     } else {
    164:       ls->stepmin = stx;
    165:       ls->stepmax = ls->step + xtrapf * (ls->step - stx);
    166:     }

    168:     /* Force the step to be within the bounds */
    169:     ls->step = PetscMax(ls->step,ls->stepmin);
    170:     ls->step = PetscMin(ls->step,ls->stepmax);

    172:     /* If an unusual termination is to occur, then let step be the lowest
    173:      point obtained thus far */
    174:     if ((stx!=0) && (((mt->bracket) && (ls->step <= ls->stepmin || ls->step >= ls->stepmax)) || ((mt->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol * ls->stepmax)) ||
    175:                      ((ls->nfeval+ls->nfgeval) >= ls->max_funcs - 1) || (mt->infoc == 0))) {
    176:       ls->step = stx;
    177:     }

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

    182:     if (ls->bounded) {
    183:       VecMedian(ls->lower, mt->work, ls->upper, mt->work);
    184:     }
    185:     if (ls->usegts) {
    186:       TaoLineSearchComputeObjectiveAndGTS(ls,mt->work,f,&dg);
    187:       g_computed=PETSC_FALSE;
    188:     } else {
    189:       TaoLineSearchComputeObjectiveAndGradient(ls,mt->work,f,g);
    190:       g_computed=PETSC_TRUE;
    191:       if (ls->bounded) {
    192:         VecDot(g,x,&dg);
    193:         VecDot(g,mt->work,&dg2);
    194:         dg = (dg2 - dg)/ls->step;
    195:       } else {
    196:         VecDot(g,s,&dg);
    197:       }
    198:     }

    200:     if (0 == i) {
    201:       ls->f_fullstep=*f;
    202:     }

    204:     if (PetscIsInfOrNanReal(*f) || PetscIsInfOrNanReal(dg)) {
    205:       /* User provided compute function generated Not-a-Number, assume
    206:        domain violation and set function value and directional
    207:        derivative to infinity. */
    208:       *f = PETSC_INFINITY;
    209:       dg = PETSC_INFINITY;
    210:     }

    212:     ftest1 = finit + ls->step * dgtest;
    213:     if (ls->bounded) {
    214:       ftest2 = finit + ls->step * dgtest * ls->ftol;
    215:     }
    216:     /* Convergence testing */
    217:     if (((*f - ftest1 <= 1.0e-10 * PetscAbsReal(finit)) &&  (PetscAbsReal(dg) + ls->gtol*dginit <= 0.0))) {
    218:       PetscInfo(ls, "Line search success: Sufficient decrease and directional deriv conditions hold\n");
    219:       ls->reason = TAOLINESEARCH_SUCCESS;
    220:       break;
    221:     }

    223:     /* Check Armijo if beyond the first breakpoint */
    224:     if (ls->bounded && (*f <= ftest2) && (ls->step >= bstepmin2)) {
    225:       PetscInfo(ls,"Line search success: Sufficient decrease.\n");
    226:       ls->reason = TAOLINESEARCH_SUCCESS;
    227:       break;
    228:     }

    230:     /* Checks for bad cases */
    231:     if (((mt->bracket) && (ls->step <= ls->stepmin||ls->step >= ls->stepmax)) || (!mt->infoc)) {
    232:       PetscInfo(ls,"Rounding errors may prevent further progress.  May not be a step satisfying\n");
    233:       PetscInfo(ls,"sufficient decrease and curvature conditions. Tolerances may be too small.\n");
    234:       ls->reason = TAOLINESEARCH_HALTED_OTHER;
    235:       break;
    236:     }
    237:     if ((ls->step == ls->stepmax) && (*f <= ftest1) && (dg <= dgtest)) {
    238:       PetscInfo1(ls,"Step is at the upper bound, stepmax (%g)\n",(double)ls->stepmax);
    239:       ls->reason = TAOLINESEARCH_HALTED_UPPERBOUND;
    240:       break;
    241:     }
    242:     if ((ls->step == ls->stepmin) && (*f >= ftest1) && (dg >= dgtest)) {
    243:       PetscInfo1(ls,"Step is at the lower bound, stepmin (%g)\n",(double)ls->stepmin);
    244:       ls->reason = TAOLINESEARCH_HALTED_LOWERBOUND;
    245:       break;
    246:     }
    247:     if ((mt->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol*ls->stepmax)){
    248:       PetscInfo1(ls,"Relative width of interval of uncertainty is at most rtol (%g)\n",(double)ls->rtol);
    249:       ls->reason = TAOLINESEARCH_HALTED_RTOL;
    250:       break;
    251:     }

    253:     /* In the first stage, we seek a step for which the modified function
    254:      has a nonpositive value and nonnegative derivative */
    255:     if ((stage1) && (*f <= ftest1) && (dg >= dginit * PetscMin(ls->ftol, ls->gtol))) {
    256:       stage1 = 0;
    257:     }

    259:     /* A modified function is used to predict the step only if we
    260:      have not obtained a step for which the modified function has a
    261:      nonpositive function value and nonnegative derivative, and if a
    262:      lower function value has been obtained but the decrease is not
    263:      sufficient */

    265:     if ((stage1) && (*f <= fx) && (*f > ftest1)) {
    266:       fm   = *f - ls->step * dgtest;    /* Define modified function */
    267:       fxm  = fx - stx * dgtest;         /* and derivatives */
    268:       fym  = fy - sty * dgtest;
    269:       dgm  = dg - dgtest;
    270:       dgxm = dgx - dgtest;
    271:       dgym = dgy - dgtest;

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

    277:       fx  = fxm + stx * dgtest; /* Reset the function and */
    278:       fy  = fym + sty * dgtest; /* gradient values */
    279:       dgx = dgxm + dgtest;
    280:       dgy = dgym + dgtest;
    281:     } else {
    282:       /* Update the interval of uncertainty and compute the new step */
    283:       Tao_mcstep(ls,&stx,&fx,&dgx,&sty,&fy,&dgy,&ls->step,f,&dg);
    284:     }

    286:     /* Force a sufficient decrease in the interval of uncertainty */
    287:     if (mt->bracket) {
    288:       if (PetscAbsReal(sty - stx) >= 0.66 * width1) ls->step = stx + 0.5*(sty - stx);
    289:       width1 = width;
    290:       width = PetscAbsReal(sty - stx);
    291:     }
    292:   }
    293:   if ((ls->nfeval+ls->nfgeval) > ls->max_funcs) {
    294:     PetscInfo2(ls,"Number of line search function evals (%D) > maximum (%D)\n",(ls->nfeval+ls->nfgeval),ls->max_funcs);
    295:     ls->reason = TAOLINESEARCH_HALTED_MAXFCN;
    296:   }

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

    301:   /* Set new solution vector and compute gradient if needed */
    302:   VecCopy(mt->work,x);
    303:   if (!g_computed) {
    304:     TaoLineSearchComputeGradient(ls,mt->work,g);
    305:   }
    306:   return(0);
    307: }

    311: PETSC_EXTERN PetscErrorCode TaoLineSearchCreate_MT(TaoLineSearch ls)
    312: {
    313:   PetscErrorCode   ierr;
    314:   TaoLineSearch_MT *ctx;

    318:   PetscNewLog(ls,&ctx);
    319:   ctx->bracket=0;
    320:   ctx->infoc=1;
    321:   ls->data = (void*)ctx;
    322:   ls->initstep = 1.0;
    323:   ls->ops->setup=0;
    324:   ls->ops->reset=0;
    325:   ls->ops->apply=TaoLineSearchApply_MT;
    326:   ls->ops->view =TaoLineSearchView_MT;
    327:   ls->ops->destroy=TaoLineSearchDestroy_MT;
    328:   ls->ops->setfromoptions=TaoLineSearchSetFromOptions_MT;
    329:   return(0);
    330: }

    332: /*
    333:      The subroutine mcstep is taken from the work of Jorge Nocedal.
    334:      this is a variant of More' and Thuente's routine.

    336:      subroutine mcstep

    338:      the purpose of mcstep is to compute a safeguarded step for
    339:      a linesearch and to update an interval of uncertainty for
    340:      a minimizer of the function.

    342:      the parameter stx contains the step with the least function
    343:      value. the parameter stp contains the current step. it is
    344:      assumed that the derivative at stx is negative in the
    345:      direction of the step. if bracket is set true then a
    346:      minimizer has been bracketed in an interval of uncertainty
    347:      with endpoints stx and sty.

    349:      the subroutine statement is

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

    354:      where

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

    362:        sty, fy, and dy are variables which specify the step,
    363:          the function, and the derivative at the other endpoint of
    364:          the interval of uncertainty. On output these parameters are
    365:          updated appropriately.

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

    372:        bracket is a logical variable which specifies if a minimizer
    373:          has been bracketed.  If the minimizer has not been bracketed
    374:          then on input bracket must be set false.  If the minimizer
    375:          is bracketed then on output bracket is set true.

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

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

    385:      subprograms called

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

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

    392: */

    396: static PetscErrorCode Tao_mcstep(TaoLineSearch ls,PetscReal *stx,PetscReal *fx,PetscReal *dx,PetscReal *sty,PetscReal *fy,PetscReal *dy,PetscReal *stp,PetscReal *fp,PetscReal *dp)
    397: {
    398:   TaoLineSearch_MT *mtP = (TaoLineSearch_MT *) ls->data;
    399:   PetscReal        gamma1, p, q, r, s, sgnd, stpc, stpf, stpq, theta;
    400:   PetscInt         bound;

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

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

    412:   if (*fp > *fx) {
    413:     /* Case 1: a higher function value.
    414:      The minimum is bracketed. If the cubic step is closer
    415:      to stx than the quadratic step, the cubic step is taken,
    416:      else the average of the cubic and quadratic steps is taken. */

    418:     mtP->infoc = 1;
    419:     bound = 1;
    420:     theta = 3 * (*fx - *fp) / (*stp - *stx) + *dx + *dp;
    421:     s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dx));
    422:     s = PetscMax(s,PetscAbsReal(*dp));
    423:     gamma1 = s*PetscSqrtScalar(PetscPowScalar(theta/s,2.0) - (*dx/s)*(*dp/s));
    424:     if (*stp < *stx) gamma1 = -gamma1;
    425:     /* Can p be 0?  Check */
    426:     p = (gamma1 - *dx) + theta;
    427:     q = ((gamma1 - *dx) + gamma1) + *dp;
    428:     r = p/q;
    429:     stpc = *stx + r*(*stp - *stx);
    430:     stpq = *stx + ((*dx/((*fx-*fp)/(*stp-*stx)+*dx))*0.5) * (*stp - *stx);

    432:     if (PetscAbsReal(stpc-*stx) < PetscAbsReal(stpq-*stx)) {
    433:       stpf = stpc;
    434:     } else {
    435:       stpf = stpc + 0.5*(stpq - stpc);
    436:     }
    437:     mtP->bracket = 1;
    438:   } else if (sgnd < 0.0) {
    439:     /* Case 2: A lower function value and derivatives of
    440:      opposite sign. The minimum is bracketed. If the cubic
    441:      step is closer to stx than the quadratic (secant) step,
    442:      the cubic step is taken, else the quadratic step is taken. */

    444:     mtP->infoc = 2;
    445:     bound = 0;
    446:     theta = 3*(*fx - *fp)/(*stp - *stx) + *dx + *dp;
    447:     s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dx));
    448:     s = PetscMax(s,PetscAbsReal(*dp));
    449:     gamma1 = s*PetscSqrtScalar(PetscPowScalar(theta/s,2.0) - (*dx/s)*(*dp/s));
    450:     if (*stp > *stx) gamma1 = -gamma1;
    451:     p = (gamma1 - *dp) + theta;
    452:     q = ((gamma1 - *dp) + gamma1) + *dx;
    453:     r = p/q;
    454:     stpc = *stp + r*(*stx - *stp);
    455:     stpq = *stp + (*dp/(*dp-*dx))*(*stx - *stp);

    457:     if (PetscAbsReal(stpc-*stp) > PetscAbsReal(stpq-*stp)) {
    458:       stpf = stpc;
    459:     } else {
    460:       stpf = stpq;
    461:     }
    462:     mtP->bracket = 1;
    463:   } else if (PetscAbsReal(*dp) < PetscAbsReal(*dx)) {
    464:     /* Case 3: A lower function value, derivatives of the
    465:      same sign, and the magnitude of the derivative decreases.
    466:      The cubic step is only used if the cubic tends to infinity
    467:      in the direction of the step or if the minimum of the cubic
    468:      is beyond stp. Otherwise the cubic step is defined to be
    469:      either stepmin or stepmax. The quadratic (secant) step is also
    470:      computed and if the minimum is bracketed then the step
    471:      closest to stx is taken, else the step farthest away is taken. */

    473:     mtP->infoc = 3;
    474:     bound = 1;
    475:     theta = 3*(*fx - *fp)/(*stp - *stx) + *dx + *dp;
    476:     s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dx));
    477:     s = PetscMax(s,PetscAbsReal(*dp));

    479:     /* The case gamma1 = 0 only arises if the cubic does not tend
    480:        to infinity in the direction of the step. */
    481:     gamma1 = s*PetscSqrtScalar(PetscMax(0.0,PetscPowScalar(theta/s,2.0) - (*dx/s)*(*dp/s)));
    482:     if (*stp > *stx) gamma1 = -gamma1;
    483:     p = (gamma1 - *dp) + theta;
    484:     q = (gamma1 + (*dx - *dp)) + gamma1;
    485:     r = p/q;
    486:     if (r < 0.0 && gamma1 != 0.0) stpc = *stp + r*(*stx - *stp);
    487:     else if (*stp > *stx)        stpc = ls->stepmax;
    488:     else                         stpc = ls->stepmin;
    489:     stpq = *stp + (*dp/(*dp-*dx)) * (*stx - *stp);

    491:     if (mtP->bracket) {
    492:       if (PetscAbsReal(*stp-stpc) < PetscAbsReal(*stp-stpq)) {
    493:         stpf = stpc;
    494:       } else {
    495:         stpf = stpq;
    496:       }
    497:     } else {
    498:       if (PetscAbsReal(*stp-stpc) > PetscAbsReal(*stp-stpq)) {
    499:         stpf = stpc;
    500:       } else {
    501:         stpf = stpq;
    502:       }
    503:     }
    504:   } else {
    505:     /* Case 4: A lower function value, derivatives of the
    506:        same sign, and the magnitude of the derivative does
    507:        not decrease. If the minimum is not bracketed, the step
    508:        is either stpmin or stpmax, else the cubic step is taken. */

    510:     mtP->infoc = 4;
    511:     bound = 0;
    512:     if (mtP->bracket) {
    513:       theta = 3*(*fp - *fy)/(*sty - *stp) + *dy + *dp;
    514:       s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dy));
    515:       s = PetscMax(s,PetscAbsReal(*dp));
    516:       gamma1 = s*PetscSqrtScalar(PetscPowScalar(theta/s,2.0) - (*dy/s)*(*dp/s));
    517:       if (*stp > *sty) gamma1 = -gamma1;
    518:       p = (gamma1 - *dp) + theta;
    519:       q = ((gamma1 - *dp) + gamma1) + *dy;
    520:       r = p/q;
    521:       stpc = *stp + r*(*sty - *stp);
    522:       stpq = *stp + (*dp/(*dp-*dx)) * (*stx - *stp);

    524:       stpf = stpc;
    525:     } else if (*stp > *stx) {
    526:       stpf = ls->stepmax;
    527:     } else {
    528:       stpf = ls->stepmin;
    529:     }
    530:   }

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

    535:   if (*fp > *fx) {
    536:     *sty = *stp;
    537:     *fy = *fp;
    538:     *dy = *dp;
    539:   } else {
    540:     if (sgnd < 0.0) {
    541:       *sty = *stx;
    542:       *fy = *fx;
    543:       *dy = *dx;
    544:     }
    545:     *stx = *stp;
    546:     *fx = *fp;
    547:     *dx = *dp;
    548:   }

    550:   /* Compute the new step and safeguard it. */
    551:   stpf = PetscMin(ls->stepmax,stpf);
    552:   stpf = PetscMax(ls->stepmin,stpf);
    553:   *stp = stpf;
    554:   if (mtP->bracket && bound) {
    555:     if (*sty > *stx) {
    556:       *stp = PetscMin(*stx+0.66*(*sty-*stx),*stp);
    557:     } else {
    558:       *stp = PetscMax(*stx+0.66*(*sty-*stx),*stp);
    559:     }
    560:   }
    561:   return(0);
    562: }