Actual source code: morethuente.c
petsc-3.10.5 2019-03-28
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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);

     12: static PetscErrorCode TaoLineSearchDestroy_MT(TaoLineSearch ls)
     13: {
     14:   PetscErrorCode   ierr;
     15:   TaoLineSearch_MT *mt;

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

     28: static PetscErrorCode TaoLineSearchSetFromOptions_MT(PetscOptionItems *PetscOptionsObject,TaoLineSearch ls)
     29: {
     32:   return(0);
     33: }

     35: static PetscErrorCode TaoLineSearchMonitor_MT(TaoLineSearch ls)
     36: {
     37:   TaoLineSearch_MT *mt = (TaoLineSearch_MT*)ls->data;
     38:   PetscErrorCode   ierr;
     39:
     41:   PetscViewerASCIIPrintf(ls->viewer, "stx: %g, fx: %g, dgx: %g\n", (double)mt->stx, (double)mt->fx, (double)mt->dgx);
     42:   PetscViewerASCIIPrintf(ls->viewer, "sty: %g, fy: %g, dgy: %g\n", (double)mt->sty, (double)mt->fy, (double)mt->dgy);
     43:   return(0);
     44: }

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

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

     56:    Info is set to 0.

     58: @ */

     60: static PetscErrorCode TaoLineSearchApply_MT(TaoLineSearch ls, Vec x, PetscReal *f, Vec g, Vec s)
     61: {
     62:   PetscErrorCode   ierr;
     63:   TaoLineSearch_MT *mt;

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

     79:
     80:   TaoLineSearchMonitor(ls, 0, *f, 0.0);

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

     86:   /* Check work vector */
     87:   if (!mt->work) {
     88:     VecDuplicate(x,&mt->work);
     89:     mt->x = x;
     90:     PetscObjectReference((PetscObject)mt->x);
     91:   } else if (x != mt->x) {
     92:     VecDestroy(&mt->work);
     93:     VecDuplicate(x,&mt->work);
     94:     PetscObjectDereference((PetscObject)mt->x);
     95:     mt->x = x;
     96:     PetscObjectReference((PetscObject)mt->x);
     97:   }

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

    115:   VecDot(g,s,&dginit);
    116:   if (PetscIsInfOrNanReal(dginit)) {
    117:     PetscInfo1(ls,"Initial Line Search step * g is Inf or Nan (%g)\n",(double)dginit);
    118:     ls->reason=TAOLINESEARCH_FAILED_INFORNAN;
    119:     return(0);
    120:   }
    121:   if (dginit >= 0.0) {
    122:     PetscInfo1(ls,"Initial Line Search step * g is not descent direction (%g)\n",(double)dginit);
    123:     ls->reason = TAOLINESEARCH_FAILED_ASCENT;
    124:     return(0);
    125:   }

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

    141:   stx = 0.0;
    142:   fx  = finit;
    143:   dgx = dginit;
    144:   sty = 0.0;
    145:   fy  = finit;
    146:   dgy = dginit;

    148:   ls->step=ls->initstep;
    149:   for (i=0; i< ls->max_funcs; i++) {
    150:     /* Set min and max steps to correspond to the interval of uncertainty */
    151:     if (mt->bracket) {
    152:       ls->stepmin = PetscMin(stx,sty);
    153:       ls->stepmax = PetscMax(stx,sty);
    154:     } else {
    155:       ls->stepmin = stx;
    156:       ls->stepmax = ls->step + xtrapf * (ls->step - stx);
    157:     }

    159:     /* Force the step to be within the bounds */
    160:     ls->step = PetscMax(ls->step,ls->stepmin);
    161:     ls->step = PetscMin(ls->step,ls->stepmax);

    163:     /* If an unusual termination is to occur, then let step be the lowest
    164:      point obtained thus far */
    165:     if ((stx!=0) && (((mt->bracket) && (ls->step <= ls->stepmin || ls->step >= ls->stepmax)) || ((mt->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol * ls->stepmax)) ||
    166:                      ((ls->nfeval+ls->nfgeval) >= ls->max_funcs - 1) || (mt->infoc == 0))) {
    167:       ls->step = stx;
    168:     }

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

    173:     if (ls->bounded) {
    174:       VecMedian(ls->lower, mt->work, ls->upper, mt->work);
    175:     }
    176:     if (ls->usegts) {
    177:       TaoLineSearchComputeObjectiveAndGTS(ls,mt->work,f,&dg);
    178:       g_computed=PETSC_FALSE;
    179:     } else {
    180:       TaoLineSearchComputeObjectiveAndGradient(ls,mt->work,f,g);
    181:       g_computed=PETSC_TRUE;
    182:       if (ls->bounded) {
    183:         VecDot(g,x,&dg);
    184:         VecDot(g,mt->work,&dg2);
    185:         dg = (dg2 - dg)/ls->step;
    186:       } else {
    187:         VecDot(g,s,&dg);
    188:       }
    189:     }
    190:
    191:     /* update bracketing parameters in the MT context for printouts in monitor */
    192:     mt->stx = stx;
    193:     mt->fx = fx;
    194:     mt->dgx = dgx;
    195:     mt->sty = sty;
    196:     mt->fy = fy;
    197:     mt->dgy = dgy;
    198:     TaoLineSearchMonitor(ls, i+1, *f, ls->step);

    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: }

    309: PETSC_EXTERN PetscErrorCode TaoLineSearchCreate_MT(TaoLineSearch ls)
    310: {
    311:   PetscErrorCode   ierr;
    312:   TaoLineSearch_MT *ctx;

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

    330: /*
    331:      The subroutine mcstep is taken from the work of Jorge Nocedal.
    332:      this is a variant of More' and Thuente's routine.

    334:      subroutine mcstep

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

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

    347:      the subroutine statement is

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

    352:      where

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

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

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

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

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

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

    383:      subprograms called

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

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

    390: */

    392: static PetscErrorCode Tao_mcstep(TaoLineSearch ls,PetscReal *stx,PetscReal *fx,PetscReal *dx,PetscReal *sty,PetscReal *fy,PetscReal *dy,PetscReal *stp,PetscReal *fp,PetscReal *dp)
    393: {
    394:   TaoLineSearch_MT *mtP = (TaoLineSearch_MT *) ls->data;
    395:   PetscReal        gamma1, p, q, r, s, sgnd, stpc, stpf, stpq, theta;
    396:   PetscInt         bound;

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

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

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

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

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

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

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

    469:     mtP->infoc = 3;
    470:     bound = 1;
    471:     theta = 3*(*fx - *fp)/(*stp - *stx) + *dx + *dp;
    472:     s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dx));
    473:     s = PetscMax(s,PetscAbsReal(*dp));

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

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

    506:     mtP->infoc = 4;
    507:     bound = 0;
    508:     if (mtP->bracket) {
    509:       theta = 3*(*fp - *fy)/(*sty - *stp) + *dy + *dp;
    510:       s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dy));
    511:       s = PetscMax(s,PetscAbsReal(*dp));
    512:       gamma1 = s*PetscSqrtScalar(PetscPowScalar(theta/s,2.0) - (*dy/s)*(*dp/s));
    513:       if (*stp > *sty) gamma1 = -gamma1;
    514:       p = (gamma1 - *dp) + theta;
    515:       q = ((gamma1 - *dp) + gamma1) + *dy;
    516:       r = p/q;
    517:       stpc = *stp + r*(*sty - *stp);
    518:       stpf = stpc;
    519:     } else if (*stp > *stx) {
    520:       stpf = ls->stepmax;
    521:     } else {
    522:       stpf = ls->stepmin;
    523:     }
    524:   }

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

    529:   if (*fp > *fx) {
    530:     *sty = *stp;
    531:     *fy = *fp;
    532:     *dy = *dp;
    533:   } else {
    534:     if (sgnd < 0.0) {
    535:       *sty = *stx;
    536:       *fy = *fx;
    537:       *dy = *dx;
    538:     }
    539:     *stx = *stp;
    540:     *fx = *fp;
    541:     *dx = *dp;
    542:   }

    544:   /* Compute the new step and safeguard it. */
    545:   stpf = PetscMin(ls->stepmax,stpf);
    546:   stpf = PetscMax(ls->stepmin,stpf);
    547:   *stp = stpf;
    548:   if (mtP->bracket && bound) {
    549:     if (*sty > *stx) {
    550:       *stp = PetscMin(*stx+0.66*(*sty-*stx),*stp);
    551:     } else {
    552:       *stp = PetscMax(*stx+0.66*(*sty-*stx),*stp);
    553:     }
    554:   }
    555:   return(0);
    556: }