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Module « scipy.optimize »

Fonction golden - module scipy.optimize

Signature de la fonction golden

def golden(func, args=(), brack=None, tol=np.float64(1.4901161193847656e-08), full_output=0, maxiter=5000) 

Description

help(scipy.optimize.golden)

Return the minimizer of a function of one variable using the golden section
method.

Given a function of one variable and a possible bracketing interval,
return a minimizer of the function isolated to a fractional precision of
tol.

Parameters
----------
func : callable func(x,*args)
    Objective function to minimize.
args : tuple, optional
    Additional arguments (if present), passed to func.
brack : tuple, optional
    Either a triple ``(xa, xb, xc)`` where ``xa < xb < xc`` and
    ``func(xb) < func(xa) and  func(xb) < func(xc)``, or a pair (xa, xb)
    to be used as initial points for a downhill bracket search (see
    `scipy.optimize.bracket`).
    The minimizer ``x`` will not necessarily satisfy ``xa <= x <= xb``.
tol : float, optional
    x tolerance stop criterion
full_output : bool, optional
    If True, return optional outputs.
maxiter : int
    Maximum number of iterations to perform.

Returns
-------
xmin : ndarray
    Optimum point.
fval : float
    (Optional output) Optimum function value.
funcalls : int
    (Optional output) Number of objective function evaluations made.

See also
--------
minimize_scalar: Interface to minimization algorithms for scalar
    univariate functions. See the 'Golden' `method` in particular.

Notes
-----
Uses analog of bisection method to decrease the bracketed
interval.

Examples
--------
We illustrate the behaviour of the function when `brack` is of
size 2 and 3, respectively. In the case where `brack` is of the
form (xa,xb), we can see for the given values, the output need
not necessarily lie in the range ``(xa, xb)``.

>>> def f(x):
...     return (x-1)**2

>>> from scipy import optimize

>>> minimizer = optimize.golden(f, brack=(1, 2))
>>> minimizer
1
>>> res = optimize.golden(f, brack=(-1, 0.5, 2), full_output=True)
>>> xmin, fval, funcalls = res
>>> f(xmin), fval
(9.925165290385052e-18, 9.925165290385052e-18)

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