Actual source code: morethuente.c

petsc-3.11.2 2019-05-18
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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: }