Actual source code: morethuente.c

petsc-3.13.2 2020-06-02
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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);

 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: static PetscErrorCode TaoLineSearchApply_MT(TaoLineSearch ls, Vec x, PetscReal *f, Vec g, Vec s)
 47: {
 48:   PetscErrorCode   ierr;
 49:   TaoLineSearch_MT *mt;

 51:   PetscReal        xtrapf = 4.0;
 52:   PetscReal        finit, width, width1, dginit, fm, fxm, fym, dgm, dgxm, dgym;
 53:   PetscReal        dgx, dgy, dg, dg2, fx, fy, stx, sty, dgtest;
 54:   PetscReal        ftest1=0.0, ftest2=0.0;
 55:   PetscInt         i, stage1,n1,n2,nn1,nn2;
 56:   PetscReal        bstepmin1, bstepmin2, bstepmax;
 57:   PetscBool        g_computed=PETSC_FALSE; /* to prevent extra gradient computation */

 65:   
 66:   TaoLineSearchMonitor(ls, 0, *f, 0.0);

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

 72:   /* Check work vector */
 73:   if (!mt->work) {
 74:     VecDuplicate(x,&mt->work);
 75:     mt->x = x;
 76:     PetscObjectReference((PetscObject)mt->x);
 77:   } else if (x != mt->x) {
 78:     VecDestroy(&mt->work);
 79:     VecDuplicate(x,&mt->work);
 80:     PetscObjectDereference((PetscObject)mt->x);
 81:     mt->x = x;
 82:     PetscObjectReference((PetscObject)mt->x);
 83:   }

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

101:   VecDot(g,s,&dginit);
102:   if (PetscIsInfOrNanReal(dginit)) {
103:     PetscInfo1(ls,"Initial Line Search step * g is Inf or Nan (%g)\n",(double)dginit);
104:     ls->reason=TAOLINESEARCH_FAILED_INFORNAN;
105:     return(0);
106:   }
107:   if (dginit >= 0.0) {
108:     PetscInfo1(ls,"Initial Line Search step * g is not descent direction (%g)\n",(double)dginit);
109:     ls->reason = TAOLINESEARCH_FAILED_ASCENT;
110:     return(0);
111:   }

113:   /* Initialization */
114:   mt->bracket = 0;
115:   stage1 = 1;
116:   finit = *f;
117:   dgtest = ls->ftol * dginit;
118:   width = ls->stepmax - ls->stepmin;
119:   width1 = width * 2.0;
120:   VecCopy(x,mt->work);
121:   /* Variable dictionary:
122:    stx, fx, dgx - the step, function, and derivative at the best step
123:    sty, fy, dgy - the step, function, and derivative at the other endpoint
124:    of the interval of uncertainty
125:    step, f, dg - the step, function, and derivative at the current step */

127:   stx = 0.0;
128:   fx  = finit;
129:   dgx = dginit;
130:   sty = 0.0;
131:   fy  = finit;
132:   dgy = dginit;

134:   ls->step=ls->initstep;
135:   for (i=0; i< ls->max_funcs; i++) {
136:     /* Set min and max steps to correspond to the interval of uncertainty */
137:     if (mt->bracket) {
138:       ls->stepmin = PetscMin(stx,sty);
139:       ls->stepmax = PetscMax(stx,sty);
140:     } else {
141:       ls->stepmin = stx;
142:       ls->stepmax = ls->step + xtrapf * (ls->step - stx);
143:     }

145:     /* Force the step to be within the bounds */
146:     ls->step = PetscMax(ls->step,ls->stepmin);
147:     ls->step = PetscMin(ls->step,ls->stepmax);

149:     /* If an unusual termination is to occur, then let step be the lowest
150:      point obtained thus far */
151:     if ((stx!=0) && (((mt->bracket) && (ls->step <= ls->stepmin || ls->step >= ls->stepmax)) || ((mt->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol * ls->stepmax)) ||
152:                      ((ls->nfeval+ls->nfgeval) >= ls->max_funcs - 1) || (mt->infoc == 0))) {
153:       ls->step = stx;
154:     }

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

159:     if (ls->bounded) {
160:       VecMedian(ls->lower, mt->work, ls->upper, mt->work);
161:     }
162:     if (ls->usegts) {
163:       TaoLineSearchComputeObjectiveAndGTS(ls,mt->work,f,&dg);
164:       g_computed=PETSC_FALSE;
165:     } else {
166:       TaoLineSearchComputeObjectiveAndGradient(ls,mt->work,f,g);
167:       g_computed=PETSC_TRUE;
168:       if (ls->bounded) {
169:         VecDot(g,x,&dg);
170:         VecDot(g,mt->work,&dg2);
171:         dg = (dg2 - dg)/ls->step;
172:       } else {
173:         VecDot(g,s,&dg);
174:       }
175:     }
176:     
177:     /* update bracketing parameters in the MT context for printouts in monitor */
178:     mt->stx = stx;
179:     mt->fx = fx;
180:     mt->dgx = dgx;
181:     mt->sty = sty;
182:     mt->fy = fy;
183:     mt->dgy = dgy;
184:     TaoLineSearchMonitor(ls, i+1, *f, ls->step);

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: }

295: /*MC 
296:    TAOLINESEARCHMT - Line-search type with cubic interpolation that satisfies both the sufficient decrease and 
297:    curvature conditions. This method can take step lengths greater than 1.

299:    More-Thuente line-search can be selected with "-tao_ls_type more-thuente".

301:    References:
302: .     1. - JORGE J. MORE AND DAVID J. THUENTE, LINE SEARCH ALGORITHMS WITH GUARANTEED SUFFICIENT DECREASE.
303:           ACM Trans. Math. Software 20, no. 3 (1994): 286-307.

305:    Level: developer

307: .seealso: TaoLineSearchCreate(), TaoLineSearchSetType(), TaoLineSearchApply()

309: .keywords: Tao, linesearch
310: M*/
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->destroy=TaoLineSearchDestroy_MT;
327:   ls->ops->setfromoptions=TaoLineSearchSetFromOptions_MT;
328:   ls->ops->monitor=TaoLineSearchMonitor_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: */

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

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

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

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

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

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

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

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

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

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

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

508:     mtP->infoc = 4;
509:     bound = 0;
510:     if (mtP->bracket) {
511:       theta = 3*(*fp - *fy)/(*sty - *stp) + *dy + *dp;
512:       s = PetscMax(PetscAbsReal(theta),PetscAbsReal(*dy));
513:       s = PetscMax(s,PetscAbsReal(*dp));
514:       gamma1 = s*PetscSqrtScalar(PetscPowScalar(theta/s,2.0) - (*dy/s)*(*dp/s));
515:       if (*stp > *sty) gamma1 = -gamma1;
516:       p = (gamma1 - *dp) + theta;
517:       q = ((gamma1 - *dp) + gamma1) + *dy;
518:       r = p/q;
519:       stpc = *stp + r*(*sty - *stp);
520:       stpf = stpc;
521:     } else if (*stp > *stx) {
522:       stpf = ls->stepmax;
523:     } else {
524:       stpf = ls->stepmin;
525:     }
526:   }

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

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

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