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
T, Tinv, S = balanced_transformation(sys)
balsys = sys.transform(T, Tinv)
# Keeping just the best state should remove the 3 noise dimensions
# Discarding the lowest state should do at least as well
for keep_states in (S.argmax(),
list(set(range(len(sys))) - set((S.argmin(), )))):
delsys = modred(balsys, keep_states)
assert delsys.order_den == np.asarray(keep_states).size
u = rng.normal(size=2000)
expected = sys.filt(u, dt)
actual = delsys.filt(u, dt)
assert rmse(expected, actual) < 1e-4
step = np.zeros(2000)
step[50:] = 1.0
dcsys = modred(balsys, keep_states, method='dc')
assert np.allclose(dcsys.dcgain, balsys.dcgain)
# use of shift related to nengo issue #938
assert not sys.has_passthrough
assert dcsys.has_passthrough
expected = shift(sys.filt(step, dt))
actual = dcsys.filt(step, dt)
assert rmse(expected, actual) < 1e-4
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_invalid_modred():
with pytest.raises(ValueError):
modred(Lowpass(0.1), 0, method='zoh')
def test_invalid_modred():
with pytest.raises(ValueError):
modred(Lowpass(0.1), 0, method='zoh')