Module « scipy.optimize »

Fonction brent - module scipy.optimize

Signature de la fonction brent

def brent(func, args=(), brack=None, tol=1.48e-08, full_output=0, maxiter=500) 

Description

brent.__doc__

    Given a function of one variable and a possible bracket, return
    the local minimum of the function isolated to a fractional precision
    of tol.

    Parameters
    ----------
    func : callable f(x,*args)
        Objective function.
    args : tuple, optional
        Additional arguments (if present).
    brack : tuple, optional
        Either a triple (xa,xb,xc) where xa<xb<xc and func(xb) <
        func(xa), func(xc) or a pair (xa,xb) which are used as a
        starting interval for a downhill bracket search (see
        `bracket`). Providing the pair (xa,xb) does not always mean
        the obtained solution will satisfy xa<=x<=xb.
    tol : float, optional
        Stop if between iteration change is less than `tol`.
    full_output : bool, optional
        If True, return all output args (xmin, fval, iter,
        funcalls).
    maxiter : int, optional
        Maximum number of iterations in solution.

    Returns
    -------
    xmin : ndarray
        Optimum point.
    fval : float
        Optimum value.
    iter : int
        Number of iterations.
    funcalls : int
        Number of objective function evaluations made.

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

    Notes
    -----
    Uses inverse parabolic interpolation when possible to speed up
    convergence of golden section method.

    Does not ensure that the minimum lies in the range specified by
    `brack`. See `fminbound`.

    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**2

    >>> from scipy import optimize

    >>> minimum = optimize.brent(f,brack=(1,2))
    >>> minimum
    0.0
    >>> minimum = optimize.brent(f,brack=(-1,0.5,2))
    >>> minimum
    -2.7755575615628914e-17