def METHOD_NAME(self):
    # set up a cosmology
    # compute image postions
    # compute J and velocity dispersion
    D_dt = self.td_cosmo._lens_cosmo.ddt
    D_d = self.td_cosmo._lens_cosmo.dd
    D_s = self.td_cosmo._lens_cosmo.ds
    D_ds = self.td_cosmo._lens_cosmo.dds
    fermat_potential_list = self.td_cosmo.fermat_potential(
        self.kwargs_lens, self.kwargs_ps
    )
    dt_list = self.td_cosmo.time_delays(
        self.kwargs_lens, self.kwargs_ps, kappa_ext=0
    )
    dt = dt_list[0] - dt_list[1]
    d_fermat = fermat_potential_list[0] - fermat_potential_list[1]
    D_dt_infered = self.td_cosmo.ddt_from_time_delay(
        d_fermat_model=d_fermat, dt_measured=dt
    )
    npt.assert_almost_equal(D_dt_infered, D_dt, decimal=5)
    r_eff = 0.5
    kwargs_lens_light = [{"Rs": r_eff * 0.551, "center_x": 0, "center_y": 0}]
    kwargs_anisotropy = {"r_ani": 1}
    anisotropy_model = "OM"
    kwargs_numerics_galkin = {
        "interpol_grid_num": 500,
        "log_integration": True,
        "max_integrate": 10,
        "min_integrate": 0.001,
    }
    self.td_cosmo.kinematics_modeling_settings(
        anisotropy_model,
        kwargs_numerics_galkin,
        analytic_kinematics=True,
        Hernquist_approx=False,
        MGE_light=False,
        MGE_mass=False,
    )
    J = self.td_cosmo.velocity_dispersion_dimension_less(
        self.kwargs_lens,
        kwargs_lens_light,
        kwargs_anisotropy,
        r_eff=r_eff,
        theta_E=self.kwargs_lens[0]["theta_E"],
        gamma=2,
    )
    J_map = self.td_cosmo.velocity_dispersion_map_dimension_less(
        self.kwargs_lens,
        kwargs_lens_light,
        kwargs_anisotropy,
        r_eff=r_eff,
        theta_E=self.kwargs_lens[0]["theta_E"],
        gamma=2,
    )
    assert len(J_map) == 1
    npt.assert_almost_equal(J_map[0] / J, 1, decimal=1)
    sigma_v2 = J * D_s / D_ds * const.c**2
    sigma_v = np.sqrt(sigma_v2) / 1000.0  # convert to [km/s]
    print(sigma_v, "test sigma_v")
    Ds_Dds = self.td_cosmo.ds_dds_from_kinematics(sigma_v, J, kappa_s=0, kappa_ds=0)
    npt.assert_almost_equal(Ds_Dds, D_s / D_ds)
    # now we perform a mass-sheet transform in the observables but leave the models identical with a convergence correction
    kappa_s = 0.5
    dt_list = self.td_cosmo.time_delays(
        self.kwargs_lens, self.kwargs_ps, kappa_ext=kappa_s
    )
    sigma_v_kappa = sigma_v * np.sqrt(1 - kappa_s)
    dt = dt_list[0] - dt_list[1]
    D_dt_infered, D_d_infered = self.td_cosmo.ddt_dd_from_time_delay_and_kinematics(
        d_fermat_model=d_fermat,
        dt_measured=dt,
        sigma_v_measured=sigma_v_kappa,
        J=J,
        kappa_s=kappa_s,
        kappa_ds=0,
        kappa_d=0,
    )
    npt.assert_almost_equal(D_dt_infered, D_dt, decimal=6)
    npt.assert_almost_equal(D_d_infered, D_d, decimal=6)