def METHOD_NAME():
    """Tests osi/lagrangian combinations"""
    # --- The dynamical systems ---
    # dimension
    ndof = 3
    # initial conditons
    q0 = np.zeros(ndof, dtype=np.float64)
    v0 = np.zeros_like(q0)
    q0[0] = 1.0
    # mass, stiffness and damping matrices
    # (diagonal values only)
    mass_diag = np.ones(ndof, dtype=np.float64)
    k_diag = np.zeros_like(mass_diag)
    c_diag = np.zeros_like(mass_diag)
    sigma = 0.2
    omega2 = 1.2
    k_diag[...] = omega2
    c_diag[...] = sigma
    ds_list = {}
    # - LagrangianLinearTIDS -
    ds_list["LTIDS+MJ"] = sk.LagrangianLinearTIDS(
        q0, v0, np.diag(mass_diag), np.diag(k_diag), np.diag(c_diag)
    )
    # - LagrangianLinearDiagonalDS -
    ds_list["LLDDS+MJ"] = sk.LagrangianLinearDiagonalDS(
        q0, v0, k_diag, c_diag, mass_diag
    )
    ds_list["LLDDS+MJB"] = sk.LagrangianLinearDiagonalDS(
        q0, v0, k_diag, c_diag, mass_diag
    )
    # no mass (i.e. implicitely equal to Id)
    ds_list["LLDDS+MJB2"] = sk.LagrangianLinearDiagonalDS(q0, v0, k_diag, c_diag)
    nb_ds = len(ds_list)
    for ds in ds_list.values():
        ds.computeForces(0.0, q0, v0)
    assert np.allclose(ds_list["LTIDS+MJ"].forces(), ds_list["LTIDS+MJ"].forces())
    # --- Interactions ---
    cor = 0.9
    nslaw = sk.NewtonImpactNSL(cor)
    hmat = np.zeros((1, ndof), dtype=np.float64)
    hmat[0, 0] = 1.0
    b = np.zeros((1), dtype=np.float64)
    b[0] = 2e-2
    relation = sk.LagrangianLinearTIR(hmat, b)
    interactions = []
    for k in range(nb_ds):
        interactions.append(sk.Interaction(nslaw, relation))
    # --- NSDS ---
    time_step = 1e-2
    tinit = 0.0
    tend = 3  # 1.5+10*time_step
    nsds = sk.NonSmoothDynamicalSystem(tinit, tend)
    # - insert ds into the model and link them with their interaction -
    ninter = 0
    for ds in ds_list.values():
        nsds.insertDynamicalSystem(ds)
        nsds.link(interactions[ninter], ds)
        ninter += 1
    # --- Simulation ---
    # - (1) OneStepIntegrators --
    theta = 0.5000001
    standard = sk.MoreauJeanOSI(theta)
    bilbao = sk.MoreauJeanBilbaoOSI()
    # -- (2) Time discretisation --
    td = sk.TimeDiscretisation(tinit, time_step)
    # -- (3) one step non smooth problem
    lcp = sk.LCP()
    # -- (4) Simulation setup with (1) (2) (3)
    simu = sk.TimeStepping(nsds, td, standard, lcp)
    # extra osi must be explicitely inserted into simu and linked to ds
    simu.associate(standard, ds_list["LTIDS+MJ"])
    simu.associate(standard, ds_list["LLDDS+MJ"])
    simu.associate(bilbao, ds_list["LLDDS+MJB"])
    simu.associate(bilbao, ds_list["LLDDS+MJB2"])
    positions = []
    velocities = []
    for ds in ds_list.values():
        positions.append(ds.q())
        velocities.append(ds.velocity())
    # number of time steps and buffer used to save results
    nb_steps = int((tend - tinit) / time_step) + 1
    data = np.zeros((nb_steps, 1 + 2 * len(ds_list)), dtype=np.float64)
    data[0, 0] = tinit
    for k in range(nb_ds):
        data[0, k * 2 + 1] = positions[k][0]
        data[0, k * 2 + 2] = velocities[k][0]
    current_iter = 1
    # --- Time loop ---
    while simu.hasNextEvent():
        simu.computeOneStep()
        data[current_iter, 0] = simu.nextTime()
        for k in range(nb_ds):
            data[current_iter, k * 2 + 1] = positions[k][0]
            data[current_iter, k * 2 + 2] = velocities[k][0]
        simu.nextStep()
        current_iter += 1
    # -- check results
    ref_pos = data[:, 1]
    ref_vel = data[:, 2]
    with_plot = False
    if with_plot:
        import matplotlib.pyplot as plt
        plt.title("position")
        plt.plot(ref_pos)
        for k in range(1, nb_ds):
            plt.plot(data[:, k * 2 + 1])
        plt.figure()
        plt.title("velocity")
        plt.plot(ref_vel)
        for k in range(1, nb_ds):
            plt.plot(data[:, k * 2 + 2])
    def test_allclose(a, b, atol, rtol):
        print(np.absolute(a - b))
        return np.absolute(a - b) <= (atol + rtol * np.absolute(b))
    # plt.plot(ref_vel)
    for k in range(1, nb_ds):
        # print('k = ', k)
        # print(test_allclose(ref_pos, data[:, k * 2 + 1], atol=time_step, rtol=1e-05))
        assert np.allclose(ref_pos, data[:, k * 2 + 1], atol=time_step)
        assert np.allclose(ref_vel, data[:, k * 2 + 2], atol=time_step)
    # plt.show()