def brenth(f,
a,
b,
args=(),
xtol=_xtol,
rtol=_rtol,
maxiter=_iter,
full_output=False,
disp=True):
"""Find root of f in [a,b].
A variation on the classic Brent routine to find a zero of the function f
between the arguments a and b that uses hyperbolic extrapolation instead of
inverse quadratic extrapolation. There was a paper back in the 1980's ...
f(a) and f(b) can not have the same signs. Generally on a par with the
brent routine, but not as heavily tested. It is a safe version of the
secant method that uses hyperbolic extrapolation. The version here is by
Chuck Harris.
Parameters
----------
f : function
Python function returning a number. f must be continuous, and f(a) and
f(b) must have opposite signs.
a : number
One end of the bracketing interval [a,b].
b : number
The other end of the bracketing interval [a,b].
xtol : number, optional
The routine converges when a root is known to lie within xtol of the
value return. Should be >= 0. The routine modifies this to take into
account the relative precision of doubles.
maxiter : number, optional
if convergence is not achieved in maxiter iterations, and error is
raised. Must be >= 0.
args : tuple, optional
containing extra arguments for the function `f`.
`f` is called by ``apply(f, (x)+args)``.
full_output : bool, optional
If `full_output` is False, the root is returned. If `full_output` is
True, the return value is ``(x, r)``, where `x` is the root, and `r` is
a RootResults object.
disp : bool, optional
If True, raise RuntimeError if the algorithm didn't converge.
Returns
-------
x0 : float
Zero of `f` between `a` and `b`.
r : RootResults (present if ``full_output = True``)
Object containing information about the convergence. In particular,
``r.converged`` is True if the routine converged.
See Also
--------
fmin, fmin_powell, fmin_cg,
fmin_bfgs, fmin_ncg : multivariate local optimizers
leastsq : nonlinear least squares minimizer
fmin_l_bfgs_b, fmin_tnc, fmin_cobyla : constrained multivariate optimizers
anneal, brute : global optimizers
fminbound, brent, golden, bracket : local scalar minimizers
fsolve : n-dimensional root-finding
brentq, brenth, ridder, bisect, newton : one-dimensional root-finding
fixed_point : scalar fixed-point finder
"""
if type(args) != type(()):
args = (args, )
r = _zeros._brenth(f, a, b, xtol, maxiter, args, full_output, disp)
return results_c(full_output, r)
def brenth(f, a, b, args=(),
xtol=_xtol, rtol=_rtol, maxiter=_iter,
full_output=False, disp=True):
"""Find root of f in [a,b].
A variation on the classic Brent routine to find a zero of the function f
between the arguments a and b that uses hyperbolic extrapolation instead of
inverse quadratic extrapolation. There was a paper back in the 1980's ...
f(a) and f(b) can not have the same signs. Generally on a par with the
brent routine, but not as heavily tested. It is a safe version of the
secant method that uses hyperbolic extrapolation. The version here is by
Chuck Harris.
Parameters
----------
f : function
Python function returning a number. f must be continuous, and f(a) and
f(b) must have opposite signs.
a : number
One end of the bracketing interval [a,b].
b : number
The other end of the bracketing interval [a,b].
xtol : number, optional
The routine converges when a root is known to lie within xtol of the
value return. Should be >= 0. The routine modifies this to take into
account the relative precision of doubles.
maxiter : number, optional
if convergence is not achieved in maxiter iterations, and error is
raised. Must be >= 0.
args : tuple, optional
containing extra arguments for the function `f`.
`f` is called by ``apply(f, (x)+args)``.
full_output : bool, optional
If `full_output` is False, the root is returned. If `full_output` is
True, the return value is ``(x, r)``, where `x` is the root, and `r` is
a RootResults object.
disp : bool, optional
If True, raise RuntimeError if the algorithm didn't converge.
Returns
-------
x0 : float
Zero of `f` between `a` and `b`.
r : RootResults (present if ``full_output = True``)
Object containing information about the convergence. In particular,
``r.converged`` is True if the routine converged.
See Also
--------
fmin, fmin_powell, fmin_cg,
fmin_bfgs, fmin_ncg : multivariate local optimizers
leastsq : nonlinear least squares minimizer
fmin_l_bfgs_b, fmin_tnc, fmin_cobyla : constrained multivariate optimizers
anneal, brute : global optimizers
fminbound, brent, golden, bracket : local scalar minimizers
fsolve : n-dimensional root-finding
brentq, brenth, ridder, bisect, newton : one-dimensional root-finding
fixed_point : scalar fixed-point finder
"""
if type(args) != type(()) :
args = (args,)
r = _zeros._brenth(f,a, b, xtol, maxiter, args, full_output, disp)
return results_c(full_output, r)
def brenth(f, a, b, args=(),
xtol=_xtol, rtol=_rtol, maxiter=_iter,
full_output=False, disp=False):
"""Find root of f in [a,b]
A variation on the classic Brent routine to find a zero
of the function f between the arguments a and b that uses
hyperbolic extrapolation instead of inverse quadratic
extrapolation. There was a paper back in the 1980's ...
f(a) and f(b) can not have the same signs. Generally on a
par with the brent routine, but not as heavily tested.
It is a safe version of the secant method that uses hyperbolic
extrapolation. The version here is by Chuck Harris.
f : Python function returning a number.
a : Number, one end of the bracketing interval.
b : Number, the other end of the bracketing interval.
xtol : Number, the routine converges when a root is known
to lie within xtol of the value return. Should be >= 0.
The routine modifies this to take into account the relative
precision of doubles.
maxiter : Number, if convergence is not achieved in
maxiter iterations, and error is raised. Must be
>= 0.
args : tuple containing extra arguments for the function f.
f is called by apply(f,(x)+args).
If full_output is False, the root is returned.
If full_output is True, the return value is (x, r), where x
is the root, and r is a RootResults object containing information
about the convergence. In particular, r.converged is True if the
the routine converged.
See also:
fmin, fmin_powell, fmin_cg,
fmin_bfgs, fmin_ncg -- multivariate local optimizers
leastsq -- nonlinear least squares minimizer
fmin_l_bfgs_b, fmin_tnc,
fmin_cobyla -- constrained multivariate optimizers
anneal, brute -- global optimizers
fminbound, brent, golden, bracket -- local scalar minimizers
fsolve -- n-dimenstional root-finding
brentq, brenth, ridder, bisect, newton -- one-dimensional root-finding
fixed_point -- scalar fixed-point finder
"""
if type(args) != type(()) :
args = (args,)
r = _zeros._brenth(f,a,b,xtol,maxiter,args,full_output,disp)
return results_c(full_output, r)
