def METHOD_NAME(self):
    lens_model_list = ["SPEP", "SHEAR_GAMMA_PSI"]
    lensModel = LensModel(lens_model_list)
    phi_G, q = 0.5, 0.8
    e1, e2 = param_util.phi_q2_ellipticity(phi_G, q)
    kwargs_lens_init = [
        {
            "theta_E": 1.0,
            "gamma": 2,
            "e1": e1,
            "e2": e2,
            "center_x": 0.1,
            "center_y": -0.1,
        },
        {"gamma_ext": 0.1, "psi_ext": 0.5},
    ]
    kwargs_fixed_lens_list = [{}, {}]
    solver = Solver(solver_type="PROFILE", lensModel=lensModel, num_images=4)
    kwargs_fixed_lens = solver.add_fixed_lens(
        kwargs_fixed_lens_list, kwargs_lens_init
    )
    assert kwargs_fixed_lens[0]["theta_E"] == kwargs_lens_init[0]["theta_E"]
    solver = Solver(solver_type="CENTER", lensModel=lensModel, num_images=2)
    kwargs_fixed_lens = solver.add_fixed_lens(
        kwargs_fixed_lens_list, kwargs_lens_init
    )
    assert kwargs_fixed_lens[0]["center_x"] == kwargs_lens_init[0]["center_x"]
    solver = Solver(solver_type="ELLIPSE", lensModel=lensModel, num_images=2)
    kwargs_fixed_lens = solver.add_fixed_lens(
        kwargs_fixed_lens_list, kwargs_lens_init
    )
    assert kwargs_fixed_lens[0]["e1"] == kwargs_lens_init[0]["e1"]
    solver = Solver(solver_type="PROFILE_SHEAR", lensModel=lensModel, num_images=4)
    kwargs_fixed_lens = solver.add_fixed_lens(
        kwargs_fixed_lens_list, kwargs_lens_init
    )
    assert kwargs_fixed_lens[0]["center_x"] == kwargs_lens_init[0]["center_x"]
    lens_model_list = ["NFW_ELLIPSE", "SHEAR"]
    lensModel = LensModel(lens_model_list)
    kwargs_lens_init = [
        {
            "alpha_Rs": 1.0,
            "Rs": 4,
            "e1": e1,
            "e2": e2,
            "center_x": 0.1,
            "center_y": -0.1,
        },
        {"e1": 0.1, "e2": 0.5},
    ]
    kwargs_fixed_lens_list = [{}, {}]
    solver = Solver(solver_type="PROFILE", lensModel=lensModel, num_images=4)
    kwargs_fixed_lens = solver.add_fixed_lens(
        kwargs_fixed_lens_list, kwargs_lens_init
    )
    assert kwargs_fixed_lens[0]["alpha_Rs"] == kwargs_lens_init[0]["alpha_Rs"]