def test_check_sys_equal():
assert not sys_equal(np.zeros(2), np.zeros(3))
assert s != z
assert not z == s
assert LinearSystem(5, analog=True) != LinearSystem(5, analog=False)
with pytest.raises(ValueError):
sys_equal(s, z)
with pytest.raises(ValueError):
ss_equal(s, z)
def test_check_sys_equal():
assert not sys_equal(np.ones(2), np.ones(3))
assert s != z
assert not z == s
assert LinearSystem(5, analog=True) != LinearSystem(5, analog=False)
with pytest.raises(ValueError):
sys_equal(s, z)
with pytest.raises(ValueError):
ss_equal(s, z)
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_zerodim_system():
sys = LinearSystem(1)
assert len(sys) == 0
assert ss_equal(sys, (0, 0, 0, 1))
# However, this following system could have dimension 0 or 1
# depending on whether we're before or after scipy 0.18
# see https://github.com/scipy/scipy/issues/5760
# TODO: ideally it would stay 0, but documenting this weirdness for now
ss_sys = LinearSystem(sys.ss)
assert len(ss_sys) in (0, 1)
def test_canonical():
sys = ([1], [1], [1], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [1, 0]], [[1], [0]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [0, 1]], [[0], [1]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [0, 1]], [[1], [0]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [0, 0]], [[1], [0]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [0, 0]], [[0], [1]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0, 1], [0, 1, 1], [1, 0, 0]], [[0], [1], [-1]],
[[1, 1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = nengo.Alpha(0.1)
csys = canonical(sys, controllable=True)
osys = canonical(sys, controllable=False)
assert ss_equal(csys, LinearSystem(sys).controllable)
assert ss_equal(osys, LinearSystem(sys).observable)
assert sys_equal(csys, osys)
assert not ss_equal(csys, osys) # different state-space realizations
A, B, C, D = csys.ss
assert sys_equal(csys, sys)
assert ss_equal(csys,
([[-20, -100], [1, 0]], [[1], [0]], [[0, 100]], [[0]]))
assert sys_equal(osys, sys)
assert ss_equal(osys,
([[-20, 1], [-100, 0]], [[0], [100]], [[1, 0]], [[0]]))
def test_non_siso_manipulation():
sys = Alpha(0.1)
A, B, C, D = sys.ss
SIMO = LinearSystem((A, B, np.eye(len(A)), [[0], [0]]))
assert not SIMO.is_SISO
assert SIMO.size_in == 1
assert SIMO.size_out == 2
assert SIMO.shape == (2, 1)
assert not SIMO.has_passthrough
assert ss_equal(_eval(SIMO), SIMO)
assert isinstance(str(SIMO), str)
assert ss_equal(canonical(SIMO), SIMO)
for sub1, sub2 in zip(sys, SIMO):
assert ss_equal(sub1, sub2)
MISO = LinearSystem((A, [[1, 1]], C, [[0, 1]]))
assert not MISO.is_SISO
assert MISO.size_in == 2
assert MISO.size_out == 1
assert MISO.shape == (1, 2)
assert MISO.has_passthrough
assert ss_equal(_eval(MISO), MISO)
assert isinstance(str(MISO), str)
MIMO = LinearSystem((A, [[1, 1]], np.eye(len(A)), np.zeros((2, 2))))
assert not MIMO.is_SISO
assert MIMO.size_in == MIMO.size_out == 2
assert MIMO.shape == (2, 2)
assert not MIMO.has_passthrough
assert ss_equal(_eval(MIMO), MIMO)
assert isinstance(str(MIMO), str)
for sub1, sub2 in zip(MISO, MIMO):
assert ss_equal(sub1, sub2)
def test_canonical():
sys = ([1], [1], [1], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [1, 0]], [[1], [0]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [0, 1]], [[0], [1]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [0, 1]], [[1], [0]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [0, 0]], [[1], [0]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0], [0, 0]], [[0], [1]], [[1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = ([[1, 0, 1], [0, 1, 1], [1, 0, 0]], [[0], [1], [-1]],
[[1, 1, 1]], [0])
assert sys_equal(canonical(sys), sys)
sys = nengo.Alpha(0.1)
csys = canonical(sys, controllable=True)
osys = canonical(sys, controllable=False)
assert sys_equal(csys, osys)
assert not ss_equal(csys, osys) # different state-space realizations
A, B, C, D = csys.ss
assert sys_equal(csys, sys)
assert ss_equal(csys,
([[-20, -100], [1, 0]], [[1], [0]], [[0, 100]], [[0]]))
assert sys_equal(osys, sys)
assert ss_equal(osys,
([[-20, 1], [-100, 0]], [[0], [100]], [[1, 0]], [[0]]))