Module « scipy.optimize »

Fonction bracket - module scipy.optimize

Signature de la fonction bracket

def bracket(func, xa=0.0, xb=1.0, args=(), grow_limit=110.0, maxiter=1000) 

Description

bracket.__doc__

    Bracket the minimum of the function.

    Given a function and distinct initial points, search in the
    downhill direction (as defined by the initial points) and return
    new points xa, xb, xc that bracket the minimum of the function
    f(xa) > f(xb) < f(xc). It doesn't always mean that obtained
    solution will satisfy xa<=x<=xb.

    Parameters
    ----------
    func : callable f(x,*args)
        Objective function to minimize.
    xa, xb : float, optional
        Bracketing interval. Defaults `xa` to 0.0, and `xb` to 1.0.
    args : tuple, optional
        Additional arguments (if present), passed to `func`.
    grow_limit : float, optional
        Maximum grow limit.  Defaults to 110.0
    maxiter : int, optional
        Maximum number of iterations to perform. Defaults to 1000.

    Returns
    -------
    xa, xb, xc : float
        Bracket.
    fa, fb, fc : float
        Objective function values in bracket.
    funcalls : int
        Number of function evaluations made.

    Examples
    --------
    This function can find a downward convex region of a function:

    >>> import matplotlib.pyplot as plt
    >>> from scipy.optimize import bracket
    >>> def f(x):
    ...     return 10*x**2 + 3*x + 5
    >>> x = np.linspace(-2, 2)
    >>> y = f(x)
    >>> init_xa, init_xb = 0, 1
    >>> xa, xb, xc, fa, fb, fc, funcalls = bracket(f, xa=init_xa, xb=init_xb)
    >>> plt.axvline(x=init_xa, color="k", linestyle="--")
    >>> plt.axvline(x=init_xb, color="k", linestyle="--")
    >>> plt.plot(x, y, "-k")
    >>> plt.plot(xa, fa, "bx")
    >>> plt.plot(xb, fb, "rx")
    >>> plt.plot(xc, fc, "bx")
    >>> plt.show()