def METHOD_NAME(
    coefficients,
    tetrads=False,
    params=None,
    tetrad_params=None,
    ax=None,
    index="radii",
    logy=False,
    **kwargs
):
    r"""
    Plot the reconstructed REE profiles of a 2D dataset of coefficients ($\lambda$s,
    and optionally $\tau$s).
    Parameters
    ----------
    coefficients : :class:`numpy.ndarray`
        2D array of $\lambda$ orthogonal polynomial coefficients, and optionally
        including $\tau$ tetrad function coefficients in the last four columns
        (where :code:`tetrads=True`).
    tetrads : :class:`bool`
        Whether the coefficient array contains tetrad coefficients ($\tau$s).
    params : :class:`list`
        List of orthongonal polynomial parameters, if defaults are not used.
    tetrad_params : :class:`list`
        List of tetrad parameters, if defaults are not used.
    ax : :class:`matplotlib.axes.Axes`
        Optionally specified axes to plot on.
    index : :class:`str`
        Index to use for the plot (one of :code:`"index", "radii", "z"`).
    logy : :class:`bool`
        Whether to log-scale the y-axis.
    Returns
    --------
    :class:`matplotlib.axes.Axes`
    """
    radii = get_ionic_radii(REE(), charge=3, coordination=8)
    # check the degree required for the lambda coefficients and get the OP parameters
    lambda_degree = coefficients.shape[1] - [0, 4][tetrads]
    params = _get_params(params or "full", degree=lambda_degree)
    # get the components and y values for the points/element locations
    _, x0, components = get_function_components(
        radii,
        params=params,
        fit_tetrads=tetrads,
        tetrad_params=tetrad_params,
    )
    ys = np.exp(coefficients @ components)
    # get the components and y values for the smooth lines
    lineradii = np.linspace(radii[0], radii[-1], 1000)
    _, x0, linecomponents = get_function_components(
        lineradii,
        params=params,
        fit_tetrads=tetrads,
        tetrad_params=tetrad_params,
    )
    liney = np.exp(coefficients @ linecomponents)
    z, linez = REE_radii_to_z(radii), REE_radii_to_z(lineradii)
    xs, linex = radii, lineradii
    ####################################################################################
    if index in ["radii", "elements"]:
        ax = plot.spider.REE_v_radii(ax=ax, logy=logy, index=index, **kwargs)
    else:
        index = "z"
        ax = plot.spider.spider(
            np.array([np.nan] * len(z)), ax=ax, indexes=z, logy=logy, **kwargs
        )
        ax.set_xticklabels(REE(dropPm=False))
        xs = z
        linex = linez
    # ys = np.exp(ys)
    # liney = np.exp(liney)
    # scatter-only spider
    plot.spider.spider(
        ys, ax=ax, indexes=xs, logy=logy, set_ticks=False, **{**kwargs, "linewidth": 0}
    )
    # line-only spider
    plot.spider.spider(
        liney,
        ax=ax,
        indexes=linex,
        logy=logy,
        set_ticks=False,
        **{**kwargs, "marker": ""}
    )
    return ax