Algorithm-LBFGS
view release on metacpan or search on metacpan
advantageous to set this parameter to a small value. A typical small
value is 0.1. This parameter shuold be greater than the ftol parameter
(1e-4) and smaller than 1.0.
xtol
The machine precision for floating-point values.
This parameter must be a positive value set by a client program to
estimate the machine precision. The line search routine will terminate
with the status code ("LBFGSERR_ROUNDING_ERROR") if the relative width
of the interval of uncertainty is less than this parameter.
orthantwise_c
Coeefficient for the L1 norm of variables.
This parameter should be set to zero for standard minimization problems.
Setting this parameter to a positive value minimizes the objective
function f(x) combined with the L1 norm |x| of the variables, f(x) +
c|x|. This parameter is the coeefficient for the |x|, i.e., c. As the L1
norm |x| is not differentiable at zero, the module modify function and
gradient evaluations from a client program suitably; a client program
LBFGSERR_INVALID_XTOL
Invalid parameter "xtol" specified.
LBFGSERR_INVALID_MAXLINESEARCH
Invalid parameter "max_linesearch" specified.
LBFGSERR_INVALID_ORTHANTWISE
Invalid parameter "orthantwise_c" specified.
LBFGSERR_OUTOFINTERVAL
The line-search step went out of the interval of uncertainty.
LBFGSERR_INCORRECT_TMINMAX
A logic error occurred; alternatively, the interval of uncertainty
became too small.
LBFGSERR_ROUNDING_ERROR
A rounding error occurred; alternatively, no line-search step satisfies
the sufficient decrease and curvature conditions.
LBFGSERR_MINIMUMSTEP
The line-search step became smaller than "min_step".
LBFGSERR_MAXIMUMSTEP
The line-search step became larger than "max_step".
LBFGSERR_MAXIMUMLINESEARCH
The line-search routine reaches the maximum number of evaluations.
LBFGSERR_MAXIMUMITERATION
The algorithm routine reaches the maximum number of iterations.
LBFGSERR_WIDTHTOOSMALL
Relative width of the interval of uncertainty is at most "xtol".
LBFGSERR_INVALIDPARAMETERS
A logic error (negative line-search step) occurred.
LBFGSERR_INCREASEGRADIENT
The current search direction increases the objective function value.
SEE ALSO
PDL, PDL::Opt::NonLinear
prev_width = 2.0 * width;
/* Copy the value of x to the work area. */
veccpy(wa, x, n);
/*
The variables stx, fx, dgx contain the values of the step,
function, and directional derivative at the best step.
The variables sty, fy, dgy contain the value of the step,
function, and derivative at the other endpoint of
the interval of uncertainty.
The variables stp, f, dg contain the values of the step,
function, and derivative at the current step.
*/
stx = sty = 0.;
fx = fy = finit;
dgx = dgy = dginit;
for (;;) {
/*
Set the minimum and maximum steps to correspond to the
present interval of uncertainty.
*/
if (brackt) {
stmin = min2(stx, sty);
stmax = max2(stx, sty);
} else {
stmin = stx;
stmax = *stp + 4.0 * (*stp - stx);
}
/* Clip the step in the range of [stpmin, stpmax]. */
}
if (*stp == param->max_step && *f <= ftest1 && dg <= dgtest) {
/* The step is the maximum value. */
return LBFGSERR_MAXIMUMSTEP;
}
if (*stp == param->min_step && (ftest1 < *f || dgtest <= dg)) {
/* The step is the minimum value. */
return LBFGSERR_MINIMUMSTEP;
}
if (brackt && (stmax - stmin) <= param->xtol * stmax) {
/* Relative width of the interval of uncertainty is at most xtol. */
return LBFGSERR_WIDTHTOOSMALL;
}
if (param->max_linesearch <= count) {
/* Maximum number of iteration. */
return LBFGSERR_MAXIMUMLINESEARCH;
}
if (*f <= ftest1 && fabs(dg) <= param->gtol * (-dginit)) {
/* The sufficient decrease condition and the directional derivative condition hold. */
return count;
}
/* Define the modified function and derivative values. */
fm = *f - *stp * dgtest;
fxm = fx - stx * dgtest;
fym = fy - sty * dgtest;
dgm = dg - dgtest;
dgxm = dgx - dgtest;
dgym = dgy - dgtest;
/*
Call update_trial_interval() to update the interval of
uncertainty and to compute the new step.
*/
uinfo = update_trial_interval(
&stx, &fxm, &dgxm,
&sty, &fym, &dgym,
stp, &fm, &dgm,
stmin, stmax, &brackt
);
/* Reset the function and gradient values for f. */
fx = fxm + stx * dgtest;
fy = fym + sty * dgtest;
dgx = dgxm + dgtest;
dgy = dgym + dgtest;
} else {
/*
Call update_trial_interval() to update the interval of
uncertainty and to compute the new step.
*/
uinfo = update_trial_interval(
&stx, &fx, &dgx,
&sty, &fy, &dgy,
stp, f, &dg,
stmin, stmax, &brackt
);
}
/*
Force a sufficient decrease in the interval of uncertainty.
*/
if (brackt) {
if (0.66 * prev_width <= fabs(sty - stx)) {
*stp = stx + 0.5 * (sty - stx);
}
prev_width = width;
width = fabs(sty - stx);
}
}
a = (u) - (v); \
(qm) = (v) + (dv) / ((dv) - (du)) * a;
/**
* Update a safeguarded trial value and interval for line search.
*
* The parameter x represents the step with the least function value.
* The parameter t represents the current step. This function assumes
* that the derivative at the point of x in the direction of the step.
* If the bracket is set to true, the minimizer has been bracketed in
* an interval of uncertainty with endpoints between x and y.
*
* @param x The pointer to the value of one endpoint.
* @param fx The pointer to the value of f(x).
* @param dx The pointer to the value of f'(x).
* @param y The pointer to the value of another endpoint.
* @param fy The pointer to the value of f(y).
* @param dy The pointer to the value of f'(y).
* @param t The pointer to the value of the trial value, t.
* @param ft The pointer to the value of f(t).
* @param dt The pointer to the value of f'(t).
if (*brackt) {
CUBIC_MINIMIZER(newt, *t, *ft, *dt, *y, *fy, *dy);
} else if (*x < *t) {
newt = tmax;
} else {
newt = tmin;
}
}
/*
Update the interval of uncertainty. This update does not
depend on the new step or the case analysis above.
- Case a: if f(x) < f(t),
x <- x, y <- t.
- Case b: if f(t) <= f(x) && f'(t)*f'(x) > 0,
x <- t, y <- y.
- Case c: if f(t) <= f(x) && f'(t)*f'(x) < 0,
x <- t, y <- x.
*/
if (*fx < *ft) {
/** Invalid parameter lbfgs_parameter_t::ftol specified. */
LBFGSERR_INVALID_FTOL,
/** Invalid parameter lbfgs_parameter_t::gtol specified. */
LBFGSERR_INVALID_GTOL,
/** Invalid parameter lbfgs_parameter_t::xtol specified. */
LBFGSERR_INVALID_XTOL,
/** Invalid parameter lbfgs_parameter_t::max_linesearch specified. */
LBFGSERR_INVALID_MAXLINESEARCH,
/** Invalid parameter lbfgs_parameter_t::orthantwise_c specified. */
LBFGSERR_INVALID_ORTHANTWISE,
/** The line-search step went out of the interval of uncertainty. */
LBFGSERR_OUTOFINTERVAL,
/** A logic error occurred; alternatively, the interval of uncertainty
became too small. */
LBFGSERR_INCORRECT_TMINMAX,
/** A rounding error occurred; alternatively, no line-search step
satisfies the sufficient decrease and curvature conditions. */
LBFGSERR_ROUNDING_ERROR,
/** The line-search step became smaller than lbfgs_parameter_t::min_step. */
LBFGSERR_MINIMUMSTEP,
/** The line-search step became larger than lbfgs_parameter_t::max_step. */
LBFGSERR_MAXIMUMSTEP,
/** The line-search routine reaches the maximum number of evaluations. */
LBFGSERR_MAXIMUMLINESEARCH,
/** The algorithm routine reaches the maximum number of iterations. */
LBFGSERR_MAXIMUMITERATION,
/** Relative width of the interval of uncertainty is at most
lbfgs_parameter_t::xtol. */
LBFGSERR_WIDTHTOOSMALL,
/** A logic error (negative line-search step) occurred. */
LBFGSERR_INVALIDPARAMETERS,
/** The current search direction increases the objective function value. */
LBFGSERR_INCREASEGRADIENT,
};
/**
* L-BFGS optimization parameters.
* greater than the \ref ftol parameter (\c 1e-4) and smaller than
* \c 1.0.
*/
lbfgsfloatval_t gtol;
/**
* The machine precision for floating-point values.
* This parameter must be a positive value set by a client program to
* estimate the machine precision. The line search routine will terminate
* with the status code (::LBFGSERR_ROUNDING_ERROR) if the relative width
* of the interval of uncertainty is less than this parameter.
*/
lbfgsfloatval_t xtol;
/**
* Coeefficient for the L1 norm of variables.
* This parameter should be set to zero for standard minimization
* problems. Setting this parameter to a positive value minimizes the
* objective function F(x) combined with the L1 norm |x| of the variables,
* {F(x) + C |x|}. This parameter is the coeefficient for the |x|, i.e.,
* C. As the L1 norm |x| is not differentiable at zero, the library
lib/Algorithm/LBFGS.pm view on Meta::CPAN
parameter shuold be greater than the ftol parameter (1e-4) and smaller than
1.0.
=head3 xtol
The machine precision for floating-point values.
This parameter must be a positive value set by a client program to estimate
the machine precision. The line search routine will terminate with the
status code (L</"LBFGSERR_ROUNDING_ERROR">) if the relative width of the
interval of uncertainty is less than this parameter.
=head3 orthantwise_c
Coeefficient for the L1 norm of variables.
This parameter should be set to zero for standard minimization problems.
Setting this parameter to a positive value minimizes the objective function
f(x) combined with the L1 norm |x| of the variables, f(x) + c|x|.
This parameter is the coeefficient for the |x|, i.e., c. As the L1
norm |x| is not differentiable at zero, the module modify function and
lib/Algorithm/LBFGS.pm view on Meta::CPAN
=head3 LBFGSERR_INVALID_MAXLINESEARCH
Invalid parameter L</"max_linesearch"> specified.
=head3 LBFGSERR_INVALID_ORTHANTWISE
Invalid parameter L</"orthantwise_c"> specified.
=head3 LBFGSERR_OUTOFINTERVAL
The line-search step went out of the interval of uncertainty.
=head3 LBFGSERR_INCORRECT_TMINMAX
A logic error occurred; alternatively, the interval of uncertainty became
too small.
=head3 LBFGSERR_ROUNDING_ERROR
A rounding error occurred; alternatively, no line-search step satisfies
the sufficient decrease and curvature conditions.
=head3 LBFGSERR_MINIMUMSTEP
The line-search step became smaller than L</"min_step">.
lib/Algorithm/LBFGS.pm view on Meta::CPAN
=head3 LBFGSERR_MAXIMUMLINESEARCH
The line-search routine reaches the maximum number of evaluations.
=head3 LBFGSERR_MAXIMUMITERATION
The algorithm routine reaches the maximum number of iterations.
=head3 LBFGSERR_WIDTHTOOSMALL
Relative width of the interval of uncertainty is at most L</"xtol">.
=head3 LBFGSERR_INVALIDPARAMETERS
A logic error (negative line-search step) occurred.
=head3 LBFGSERR_INCREASEGRADIENT
The current search direction increases the objective function value.
=head1 SEE ALSO
PERL_MAGIC_qr|5.007002||p
PERL_MAGIC_regdata|5.007002||p
PERL_MAGIC_regdatum|5.007002||p
PERL_MAGIC_regex_global|5.007002||p
PERL_MAGIC_shared_scalar|5.007003||p
PERL_MAGIC_shared|5.007003||p
PERL_MAGIC_sigelem|5.007002||p
PERL_MAGIC_sig|5.007002||p
PERL_MAGIC_substr|5.007002||p
PERL_MAGIC_sv|5.007002||p
PERL_MAGIC_taint|5.007002||p
PERL_MAGIC_tiedelem|5.007002||p
PERL_MAGIC_tiedscalar|5.007002||p
PERL_MAGIC_tied|5.007002||p
PERL_MAGIC_utf8|5.008001||p
PERL_MAGIC_uvar_elem|5.007003||p
PERL_MAGIC_uvar|5.007002||p
PERL_MAGIC_vec|5.007002||p
PERL_MAGIC_vstring|5.008001||p
PERL_QUAD_MAX|5.004000||p
PERL_QUAD_MIN|5.004000||p
PL_rsfp_filters|5.004050||p
PL_rsfp|5.004050||p
PL_rs|||n
PL_stack_base|5.004050||p
PL_stack_sp|5.004050||p
PL_stdingv|5.004050||p
PL_sv_arenaroot|5.004050||p
PL_sv_no|5.004050||pn
PL_sv_undef|5.004050||pn
PL_sv_yes|5.004050||pn
PL_tainted|5.004050||p
PL_tainting|5.004050||p
POPi|||n
POPl|||n
POPn|||n
POPpbytex||5.007001|n
POPpx||5.005030|n
POPp|||n
POPs|||n
PTR2IV|5.006000||p
PTR2NV|5.006000||p
PTR2UV|5.006000||p
do_trans|||
do_vecget|||
do_vecset|||
do_vop|||
docatch_body|||
docatch|||
doeval|||
dofile|||
dofindlabel|||
doform|||
doing_taint||5.008001|n
dooneliner|||
doopen_pm|||
doparseform|||
dopoptoeval|||
dopoptolabel|||
dopoptoloop|||
dopoptosub_at|||
dopoptosub|||
dounwind|||
dowantarray|||
magic_freeovrld|||
magic_freeregexp|||
magic_getarylen|||
magic_getdefelem|||
magic_getglob|||
magic_getnkeys|||
magic_getpack|||
magic_getpos|||
magic_getsig|||
magic_getsubstr|||
magic_gettaint|||
magic_getuvar|||
magic_getvec|||
magic_get|||
magic_killbackrefs|||
magic_len|||
magic_methcall|||
magic_methpack|||
magic_nextpack|||
magic_regdata_cnt|||
magic_regdatum_get|||
magic_setfm|||
magic_setglob|||
magic_setisa|||
magic_setmglob|||
magic_setnkeys|||
magic_setpack|||
magic_setpos|||
magic_setregexp|||
magic_setsig|||
magic_setsubstr|||
magic_settaint|||
magic_setutf8|||
magic_setuvar|||
magic_setvec|||
magic_set|||
magic_sizepack|||
magic_wipepack|||
magicname|||
make_trie|||
malloced_size|||n
malloc||5.007002|n
sv_setref_pvn|||
sv_setref_pv|||
sv_setref_uv||5.007001|
sv_setsv_cow|||
sv_setsv_flags||5.007002|
sv_setsv_mg|5.006000||p
sv_setsv_nomg|5.007002||p
sv_setsv|||
sv_setuv_mg|5.006000||p
sv_setuv|5.006000||p
sv_tainted||5.004000|
sv_taint||5.004000|
sv_true||5.005000|
sv_unglob|||
sv_uni_display||5.007003|
sv_unmagic|||
sv_unref_flags||5.007001|
sv_unref|||
sv_untaint||5.004000|
sv_upgrade|||
sv_usepvn_mg|5.006000||p
sv_usepvn|||
sv_utf8_decode||5.006000|
sv_utf8_downgrade||5.006000|
sv_utf8_encode||5.006000|
sv_utf8_upgrade_flags||5.007002|
sv_utf8_upgrade||5.007001|
sv_uv|5.006000||p
sv_vcatpvf_mg|5.006000|5.004000|p
sv_vsetpvf_mg|5.006000|5.004000|p
sv_vsetpvfn||5.004000|
sv_vsetpvf|5.006000|5.004000|p
svtype|||
swallow_bom|||
swash_fetch||5.007002|
swash_init||5.006000|
sys_intern_clear|||
sys_intern_dup|||
sys_intern_init|||
taint_env|||
taint_proper|||
tmps_grow||5.006000|
toLOWER|||
toUPPER|||
to_byte_substr|||
to_uni_fold||5.007003|
to_uni_lower_lc||5.006000|
to_uni_lower||5.007003|
to_uni_title_lc||5.006000|
to_uni_title||5.007003|
to_uni_upper_lc||5.006000|
# define PL_ppaddr ppaddr
# define PL_rsfp_filters rsfp_filters
# define PL_rsfp rsfp
# define PL_stack_base stack_base
# define PL_stack_sp stack_sp
# define PL_stdingv stdingv
# define PL_sv_arenaroot sv_arenaroot
# define PL_sv_no sv_no
# define PL_sv_undef sv_undef
# define PL_sv_yes sv_yes
# define PL_tainted tainted
# define PL_tainting tainting
/* Replace: 0 */
#endif
#ifndef PERL_UNUSED_DECL
# ifdef HASATTRIBUTE
# if (defined(__GNUC__) && defined(__cplusplus)) || defined(__INTEL_COMPILER)
# define PERL_UNUSED_DECL
# else
# define PERL_UNUSED_DECL __attribute__((unused))
# endif
#endif
#ifndef PERL_MAGIC_sig
# define PERL_MAGIC_sig 'S'
#endif
#ifndef PERL_MAGIC_sigelem
# define PERL_MAGIC_sigelem 's'
#endif
#ifndef PERL_MAGIC_taint
# define PERL_MAGIC_taint 't'
#endif
#ifndef PERL_MAGIC_uvar
# define PERL_MAGIC_uvar 'U'
#endif
#ifndef PERL_MAGIC_uvar_elem
# define PERL_MAGIC_uvar_elem 'u'
#endif
( run in 0.423 second using v1.01-cache-2.11-cpan-d6f9594c0a5 )