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
balsys, S = balreal(sys)
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)
def test_modred(rng):
dt = 0.001
isys = Lowpass(0.05)
noise = 0.5*Lowpass(0.01) + 0.5*Alpha(0.005)
p = 0.999
sys = p*isys + (1-p)*noise
balsys, S = balreal(sys)
delsys = modred(balsys, S.argmax())
assert delsys.order_den == 1
u = rng.normal(size=2000)
expected = apply_filter(sys, dt, u)
actual = apply_filter(delsys, dt, u)
assert rmse(expected, actual) < 1e-4
step = np.zeros(2000)
step[50:] = 1.0
dcsys = modred(balsys, S.argmax(), method='dc')
expected = apply_filter(sys, dt, step)
actual = apply_filter(dcsys, dt, step)
assert rmse(expected, actual) < 1e-4
def test_hankel(sys):
assert np.allclose(hankel(sys), balreal(sys)[1])
