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
    -------
    root : float
        Root 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
    --------
    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

    References
    ----------
    .. [BusAndDekker1975]
       Bus, J. C. P., Dekker, T. J.,
       "Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero
       of a Function", ACM Transactions on Mathematical Software, Vol. 1, Issue
       4, Dec. 1975, pp. 330-345. Section 3: "Algorithm M".
       :doi:`10.1145/355656.355659`

    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

    r