def test_linearfilter_y0(allclose):
# --- y0 sets initial state correctly for high-order filter
synapse = LinearFilter(butter_num, butter_den, analog=False)
v = 9.81
x = v * np.ones(10)
assert allclose(synapse.filt(x, y0=v), v)
assert not allclose(synapse.filt(x, y0=0), v, record_rmse=False)
# --- y0 does not work for high-order synapse when DC gain is zero
synapse = LinearFilter([1, 0], [1, 1])
with pytest.raises(ValidationError, match="Cannot solve for state"):
synapse.filt(np.ones(10), y0=1)
def test_linearfilter(Simulator, plt, seed, allclose):
dt = 1e-3
synapse = LinearFilter(butter_num, butter_den, analog=False)
t, x, yhat = run_synapse(Simulator, seed, synapse, dt=dt)
y = synapse.filt(x, dt=dt, y0=0)
assert signals_allclose(t, y, yhat, delay=dt, plt=plt, allclose=allclose)
def test_direct(Simulator, plt, seed, allclose):
dt = 1e-3
a = 0.7
synapse = LinearFilter([a], [1], analog=False)
t, x, yhat = run_synapse(Simulator, seed, synapse, dt=dt)
y = synapse.filt(x, dt=dt, y0=0)
assert signals_allclose(t, y, yhat, delay=dt, allclose=allclose)
assert signals_allclose(t, a * x, y, plt=plt, allclose=allclose)
def test_linearfilter(Simulator, plt, seed):
dt = 1e-3
# The following num, den are for a 4th order analog Butterworth filter,
# generated with `scipy.signal.butter(4, 0.2, analog=False)`
num = np.array(
[0.00482434, 0.01929737, 0.02894606, 0.01929737, 0.00482434])
den = np.array([1., -2.36951301, 2.31398841, -1.05466541, 0.18737949])
synapse = LinearFilter(num, den, analog=False)
t, x, yhat = run_synapse(Simulator, seed, synapse, dt=dt)
y = synapse.filt(x, dt=dt, y0=0)
assert allclose(t, y, yhat, delay=dt, plt=plt)
def test_linear_analog(Simulator, seed):
dt = 1e-3
# The following num, den are for a 4th order analog Butterworth filter,
# generated with `scipy.signal.butter(4, 200, analog=True)`
num = np.array([1.60000000e+09])
den = np.array([1.00000000e+00, 5.22625186e+02, 1.36568542e+05,
2.09050074e+07, 1.60000000e+09])
synapse = LinearFilter(num, den, analog=True)
t, x, yhat = run_synapse(Simulator, seed, synapse, dt=dt)
y = synapse.filt(x, dt=dt, y0=0)
assert allclose(t, y, yhat, delay=dt, atol=5e-4)
def test_linearfilter(Simulator, plt, seed):
dt = 1e-3
# The following num, den are for a 4th order analog Butterworth filter,
# generated with `scipy.signal.butter(4, 0.2, analog=False)`
num = np.array(
[0.00482434, 0.01929737, 0.02894606, 0.01929737, 0.00482434])
den = np.array([1., -2.36951301, 2.31398841, -1.05466541, 0.18737949])
synapse = LinearFilter(num, den, analog=False)
t, x, yhat = run_synapse(Simulator, seed, synapse, dt=dt)
y = synapse.filt(x, dt=dt, y0=0)
assert allclose(t, y, yhat, delay=dt, plt=plt)
def test_linear_analog(Simulator, seed):
dt = 1e-3
# The following num, den are for a 4th order analog Butterworth filter,
# generated with `scipy.signal.butter(4, 200, analog=True)`
num = np.array([1.60000000e09])
den = np.array(
[1.00000000e00, 5.22625186e02, 1.36568542e05, 2.09050074e07, 1.60000000e09]
)
synapse = LinearFilter(num, den, analog=True)
t, x, yhat = run_synapse(Simulator, seed, synapse, dt=dt)
y = synapse.filt(x, dt=dt, y0=0)
assert signals_allclose(t, y, yhat, delay=dt, atol=5e-4)
def test_lti_lowpass(rng, plt):
dt = 1e-3
tend = 3.
t = dt * np.arange(tend / dt)
nt = len(t)
tau = 1e-2
lti = LinearFilter([1], [tau, 1])
u = rng.normal(size=(nt, 10))
x = Lowpass(tau).filt(u, dt=dt)
y = lti.filt(u, dt=dt)
plt.plot(t, x[:, 0], label="Lowpass")
plt.plot(t, y[:, 0], label="LTI")
plt.legend(loc="best")
assert np.allclose(x, y)
def test_lti_lowpass(rng, plt):
dt = 1e-3
tend = 3.
t = dt * np.arange(tend / dt)
nt = len(t)
tau = 1e-2
lti = LinearFilter([1], [tau, 1])
u = rng.normal(size=(nt, 10))
x = Lowpass(tau).filt(u, dt=dt)
y = lti.filt(u, dt=dt)
plt.plot(t, x[:, 0], label="Lowpass")
plt.plot(t, y[:, 0], label="LTI")
plt.legend(loc="best")
assert np.allclose(x, y)
def test_zero_matrices(Simulator, zero, seed):
dt = 1e-3
A = np.diag(np.ones(2) * dt)
B = np.zeros((2, 1))
B[0] = 1
C = np.ones((1, 2))
D = np.ones((1, ))
if zero == "C":
C[...] = 0
elif zero == "D":
D[...] = 0
num, den = ss2tf(A, B, C, D)
num = num.flatten()
synapse = LinearFilter(num, den, analog=False)
t, x, yhat = run_synapse(Simulator, seed, synapse, dt=dt)
y = synapse.filt(x, dt=dt, y0=0)
assert allclose(t, y, yhat, delay=dt * 2 if zero == "D" else dt, atol=5e-5)
def test_zero_matrices(Simulator, zero, seed):
dt = 1e-3
A = np.diag(np.ones(2) * dt)
B = np.zeros((2, 1))
B[0] = 1
C = np.ones((1, 2))
D = np.ones((1,))
if zero == "C":
C[...] = 0
elif zero == "D":
D[...] = 0
num, den = ss2tf(A, B, C, D)
num = num.flatten()
synapse = LinearFilter(num, den, analog=False)
t, x, yhat = run_synapse(Simulator, seed, synapse, dt=dt)
y = synapse.filt(x, dt=dt, y0=0)
assert allclose(t, y, yhat, delay=dt * 2 if zero == "D" else dt, atol=5e-5)
