def test_similarity_transform():
sys = Alpha(0.1)
TA, TB, TC, TD = sys.transform(np.eye(2), np.eye(2)).ss
A, B, C, D = sys2ss(sys)
assert np.allclose(A, TA)
assert np.allclose(B, TB)
assert np.allclose(C, TC)
assert np.allclose(D, TD)
T = [[1, 1], [-0.5, 0]]
rsys = sys.transform(T)
assert ss_equal(rsys, sys.transform(T, inv(T)))
TA, TB, TC, TD = rsys.ss
assert not np.allclose(A, TA)
assert not np.allclose(B, TB)
assert not np.allclose(C, TC)
assert np.allclose(D, TD)
assert sys_equal(sys, (TA, TB, TC, TD))
length = 1000
dt = 0.001
x_old = np.asarray(
[sub.impulse(length=length, dt=dt) for sub in sys])
x_new = np.asarray(
[sub.impulse(length=length, dt=dt) for sub in rsys])
# dot(T, x_new(t)) = x_old(t)
assert np.allclose(np.dot(T, x_new), x_old)
def test_identity(radii):
sys = Alpha(0.1)
identity = Identity()
assert repr(identity) == "Identity()"
I = np.eye(len(sys))
realize_result = identity(sys, radii)
assert realize_result.sys is sys
assert np.allclose(realize_result.T, I * radii)
assert np.allclose(realize_result.Tinv, inv(I * radii))
rsys = realize_result.realization
assert ss_equal(rsys, sys.transform(realize_result.T))
# Check that it's still the same system, even though different matrices
assert sys_equal(sys, rsys)
if radii == 1:
assert ss_equal(sys, rsys)
else:
assert not np.allclose(sys.B, rsys.B)
assert not np.allclose(sys.C, rsys.C)
# Check that the state vectors have scaled power
assert np.allclose(state_norm(sys) / radii, state_norm(rsys))
def test_func_realize(radii):
sys = Alpha(0.1)
T = np.asarray([[1., 2.], [0, -1.]])
for Tinv in (None, inv(T)):
realize_result = _realize(sys, radii, T, Tinv)
assert realize_result.sys is sys
assert np.allclose(inv(realize_result.T), realize_result.Tinv)
rsys = realize_result.realization
assert ss_equal(rsys, sys.transform(realize_result.T))
# Check that the state vector are related by T
length = 1000
dt = 0.001
x_old = np.asarray([sub.impulse(length, dt) for sub in sys])
x_new = np.asarray([sub.impulse(length, dt) for sub in rsys])
r = np.atleast_2d(np.asarray(radii).T).T
assert np.allclose(np.dot(T, x_new * r), x_old)