test_lyapunov.py 文件源码

def test_balreal():
    isys = Lowpass(0.05)
    noise = 0.5*Lowpass(0.01) + 0.5*Alpha(0.005)
    p = 0.8
    sys = p*isys + (1-p)*noise

    T, Tinv, S = balanced_transformation(sys)
    assert np.allclose(inv(T), Tinv)
    assert np.allclose(S, hsvd(sys))

    balsys = sys.transform(T, Tinv)
    assert balsys == sys

    assert np.all(S >= 0)
    assert np.all(S[0] > 0.3)
    assert np.all(S[1:] < 0.05)
    assert np.allclose(sorted(S, reverse=True), S)

    P = control_gram(balsys)
    Q = observe_gram(balsys)

    diag = np.diag_indices(len(P))
    offdiag = np.ones_like(P, dtype=bool)
    offdiag[diag] = False
    offdiag = np.where(offdiag)

    assert np.allclose(P[diag], S)
    assert np.allclose(P[offdiag], 0)
    assert np.allclose(Q[diag], S)
    assert np.allclose(Q[offdiag], 0)