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 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_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]]))
def __call__(self, sys, radii=1.0):
return scale_state(canonical(sys, controllable=False), radii=radii), {}
