Module « scipy.optimize »

Fonction ridder - module scipy.optimize

Signature de la fonction ridder

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

Description

ridder.__doc__

    Find a root of a function in an interval using Ridder's method.

    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.
    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``.
    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.

    See Also
    --------
    brentq, brenth, bisect, newton : 1-D root-finding
    fixed_point : scalar fixed-point finder

    Notes
    -----
    Uses [Ridders1979]_ method to find a zero of the function `f` between the
    arguments `a` and `b`. Ridders' method is faster than bisection, but not
    generally as fast as the Brent routines. [Ridders1979]_ provides the
    classic description and source of the algorithm. A description can also be
    found in any recent edition of Numerical Recipes.

    The routine used here diverges slightly from standard presentations in
    order to be a bit more careful of tolerance.

    References
    ----------
    .. [Ridders1979]
       Ridders, C. F. J. "A New Algorithm for Computing a
       Single Root of a Real Continuous Function."
       IEEE Trans. Circuits Systems 26, 979-980, 1979.

    Examples
    --------

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

    >>> from scipy import optimize

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

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