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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def correct_rytov_output(radius, sphere_index, medium_index, radius_sampling):
 r"""Error-correction of refractive index and radius for Rytov This method corrects the fitting results for `radius` :math:`r_\text{Ryt}` and `sphere_index` :math:`n_\text{Ryt}` obtained using :func:`qpsphere.models.rytov` using the approach described in :cite:`Mueller2018` (eqns. 3,4, and 5). .. math:: n_\text{Ryt-SC} &= n_\text{Ryt} + n_\text{med} \cdot \left( a_n x^2 + b_n x + c_n \right) r_\text{Ryt-SC} &= r_\text{Ryt} \cdot \left( a_r x^2 +b_r x + c_r \right) &\text{with} x = \frac{n_\text{Ryt}}{n_\text{med}} - 1 The correction factors are given in :data:`qpsphere.models.mod_rytov_sc.RSC_PARAMS`. Parameters radius: float Fitted radius of the sphere :math:`r_\text{Ryt}` [m] sphere_index: float Fitted refractive index of the sphere :math:`n_\text{Ryt}` medium_index: float Refractive index of the surrounding medium :math:`n_\text{med}` radius_sampling: int Number of pixels used to sample the sphere radius when computing the Rytov field. Returns ------- radius_sc: float Systematically corrected radius of the sphere :math:`r_\text{Ryt-SC}` [m] sphere_index_sc: float Systematically corrected refractive index of the sphere :math:`n_\text{Ryt-SC}` See Also -------- correct_rytov_sc_input: the inverse of this method """

    params = get_params(radius_sampling)

    x = sphere_index / medium_index - 1

    radius_sc = radius * (params["ra"] * x**2
                          + params["rb"] * x
                          + params["rc"])

    sphere_index_sc = sphere_index + medium_index * (params["na"] * x**2
                                                     + params["nb"] * x)

    return radius_sc, sphere_index_sc