Module « scipy.optimize »

Fonction brenth - module scipy.optimize

Signature de la fonction brenth

def brenth(f, a, b, args=(), xtol=2e-12, rtol=8.881784197001252e-16, maxiter=100, full_output=False, disp=True) 

Description

brenth.__doc__

Find a root of a function in a bracketing interval using Brent's
    method with hyperbolic extrapolation.

    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) cannot 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 : scalar
        One end of the bracketing interval [a,b].
    b : scalar
        The other end of the bracketing interval [a,b].
    xtol : number, optional
        The computed root ``x0`` will satisfy ``np.allclose(x, x0,
        atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
        parameter must be nonnegative. As with `brentq`, for nice
        functions the method will often satisfy the above condition
        with ``xtol/2`` and ``rtol/2``.
    rtol : number, optional
        The computed root ``x0`` will satisfy ``np.allclose(x, x0,
        atol=xtol, rtol=rtol)``, where ``x`` is the exact root. The
        parameter cannot be smaller than its default value of
        ``4*np.finfo(float).eps``. As with `brentq`, for nice functions
        the method will often satisfy the above condition with
        ``xtol/2`` and ``rtol/2``.
    maxiter : int, optional
        If convergence is not achieved in `maxiter` iterations, an 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.
        Otherwise, the convergence status is recorded in any `RootResults`
        return object.

    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.

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

    >>> from scipy import optimize

    >>> root = optimize.brenth(f, -2, 0)
    >>> root
    -1.0

    >>> root = optimize.brenth(f, 0, 2)
    >>> root
    1.0

    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

    basinhopping, differential_evolution, brute : global optimizers

    fminbound, brent, golden, bracket : local scalar minimizers

    fsolve : N-D root-finding

    brentq, brenth, ridder, bisect, newton : 1-D root-finding

    fixed_point : scalar fixed-point finder