def test_l1_norm_known():
# Check that Lowpass has a norm of exactly 1
l1, rtol = l1_norm(Lowpass(0.1))
assert np.allclose(l1, 1)
assert np.allclose(rtol, 0)
# Check that passthrough is handled properly
assert np.allclose(l1_norm(Lowpass(0.1) + 5)[0], 6)
# Check that Alpha scaled by a has a norm of approximately abs(a)
for a in (-2, 3):
for desired_rtol in (1e-1, 1e-2, 1e-4, 1e-8):
l1, rtol = l1_norm(a*Alpha(0.1), rtol=desired_rtol)
assert np.allclose(l1, abs(a), rtol=rtol)
assert rtol <= desired_rtol
def test_l1_norm_known():
# Check that Lowpass has a norm of exactly 1
l1, rtol = l1_norm(Lowpass(0.1))
assert np.allclose(l1, 1)
assert np.allclose(rtol, 0)
# Check that passthrough is handled properly
assert np.allclose(l1_norm(Lowpass(0.1) + 5)[0], 6)
assert np.allclose(l1_norm(Lowpass(0.1) - 5)[0], 6)
# Check that Alpha scaled by a has a norm of approximately abs(a)
for a in (-2, 3):
for desired_rtol in (1e-1, 1e-2, 1e-4, 1e-8):
l1, rtol = l1_norm(a * Alpha(0.1), rtol=desired_rtol)
assert np.allclose(l1, abs(a), rtol=rtol)
assert rtol <= desired_rtol
def __call__(self, sys, radii=1):
"""Produces a :class:`.RealizerResult` scaled by the ``radii``."""
# TODO: this also recomputes many subcalculations in l1_norm
sys = LinearSystem(sys)
T = np.diag(
np.atleast_1d(
np.squeeze([
l1_norm(sub, rtol=self.rtol, max_length=self.max_length)[0]
for sub in sys
])))
return _realize(sys, radii, T)
def test_l1_norm_unknown(sys):
# These impulse responses have zero-crossings which makes computing their
# exact L1-norm infeasible without simulation.
dt = 0.0001
length = 500000
response = impulse(sys, dt=dt, length=length)
assert np.allclose(response[-10:], 0)
l1_est = np.sum(abs(response) * dt)
desired_rtol = 1e-6
l1, rtol = l1_norm(sys, rtol=desired_rtol, max_length=2*length)
assert np.allclose(l1, l1_est, rtol=1e-3)
assert rtol <= desired_rtol
def test_l1_norm_unknown(sys):
# These impulse responses have zero-crossings which makes computing their
# exact L1-norm infeasible without simulation.
dt = 0.0001
length = 500000
response = sys.impulse(length, dt)
assert np.allclose(response[-10:], 0)
l1_est = np.sum(abs(response) * dt)
desired_rtol = 1e-6
l1, rtol = l1_norm(sys, rtol=desired_rtol, max_length=2 * length)
assert np.allclose(l1, l1_est, rtol=1e-3)
assert rtol <= desired_rtol
def radii(self, sys):
# TODO: this also recomputes many subcalculations in l1_norm
return np.squeeze(
[l1_norm(sub, rtol=self.rtol, max_length=self.max_length)[0] for sub in decompose_states(sys)]
)
def test_l1_norm_bad():
with pytest.raises(ValueError):
l1_norm(~z)
with pytest.raises(ValueError):
l1_norm(~s)
def test_l1_norm_bad():
with pytest.raises(ValueError):
l1_norm(~z)
with pytest.raises(ValueError):
l1_norm(~s)