def test_State_algebra_mul_rmul_mimo_siso():
sta_siso = State(5)
sta_mimo = State(2.0 * np.eye(3))
dyn_siso = State(haroldcompanion([1, 3, 3, 1]), e_i(3, -1), e_i(3, 1).T)
dyn_mimo = State(haroldcompanion([1, 3, 3, 1]), e_i(3, [1, 2]), np.eye(3))
dyn_mimo_sq = State(haroldcompanion([1, 3, 3, 1]), np.eye(3), np.eye(3))
G = dyn_siso * dyn_mimo
J = np.array([[0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 1., 0., 1., 0., 0., 0., 0., 0., 0.],
[-1., -3., -3., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
[0., 0., 0., -1., -3., -3., 0., 0., 0., 1., 0.],
[0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., -1., -3., -3., 0., 1.],
[1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.]])
assert_array_almost_equal(concatenate_state_matrices(G), J)
G = dyn_mimo * dyn_siso
assert_array_almost_equal(concatenate_state_matrices(G), J)
G = dyn_mimo * sta_siso
assert_array_almost_equal(G.b, 5 * dyn_mimo.b)
assert_array_almost_equal(G.d, 5 * dyn_mimo.d)
assert_raises(ValueError, sta_mimo.__add__, dyn_mimo)
F = sta_mimo @ dyn_mimo
J = np.array([[0., 1., 0., 0., 0.], [0., 0., 1., 1., 0.],
[-1., -3., -3., 0., 1.], [2., 0., 0., 0., 0.],
[0., 2., 0., 0., 0.], [0., 0., 2., 0., 0.]])
assert_array_almost_equal(concatenate_state_matrices(F), J)
assert_almost_equal((dyn_mimo_sq + sta_mimo).d, 2 * np.eye(3))
def test_State_algebra_mimo_siso():
static_siso_state = State(5)
static_mimo_state = State(2.0*np.eye(3))
dynamic_siso_state = State(haroldcompanion([1, 3, 3, 1]),
e_i(3, -1),
e_i(3, 1).T,
0)
dynamic_mimo_state = State(haroldcompanion([1, 3, 3, 1]),
e_i(3, [1, 2]),
np.eye(3),
np.zeros((3, 2)))
dynamic_square_state = State(haroldcompanion([1, 3, 3, 1]),
np.eye(3),
np.eye(3),
np.zeros((3, 3))
)
assert_raises(IndexError, dynamic_siso_state.__mul__, static_mimo_state)
assert_raises(IndexError, dynamic_siso_state.__add__, static_mimo_state)
assert_raises(IndexError, static_mimo_state.__add__, dynamic_mimo_state)
assert_raises(IndexError, static_mimo_state.__add__, static_siso_state)
assert_raises(IndexError, static_mimo_state.__mul__, static_siso_state)
F = static_mimo_state @ dynamic_mimo_state
assert_almost_equal(F.c, np.eye(3)*2.0)
assert_almost_equal((dynamic_square_state + static_mimo_state).d,
2*np.eye(3))
def test_State_algebra_add_radd():
sta_siso = State(5)
sta_mimo = State(2.0 * np.eye(3))
dyn_siso = State(haroldcompanion([1, 3, 3, 1]), e_i(3, -1), e_i(3, 1).T)
dyn_mimo = State(haroldcompanion([1, 3, 3, 1]), e_i(3, [1, 2]), np.eye(3))
dyn_mimo_sq = State(haroldcompanion([1, 3, 3, 1]), np.eye(3), np.eye(3))
G = dyn_mimo + sta_siso
assert_array_almost_equal(G.d,
sta_siso.to_array() * np.ones(dyn_mimo.shape))
assert_raises(ValueError, dyn_mimo.__add__, sta_mimo)
G = dyn_mimo_sq + sta_mimo
assert_array_almost_equal(G.d, 2. * np.eye(3))
G = dyn_mimo + dyn_siso
J = np.array([[0., 1., 0., 0., 0., 0., 0., 0.],
[0., 0., 1., 0., 0., 0., 1., 0.],
[-1., -3., -3., 0., 0., 0., 0., 1.],
[0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., -1., -3., -3., 1., 1.],
[1., 0., 0., 0., 1., 0., 0., 0.],
[0., 1., 0., 0., 1., 0., 0., 0.],
[0., 0., 1., 0., 1., 0., 0., 0.]])
assert_array_almost_equal(concatenate_state_matrices(G), J)
assert_raises(ValueError, dyn_mimo.__add__, dyn_mimo_sq)
assert_raises(ValueError, dyn_mimo.__sub__, dyn_mimo_sq)
assert_raises(ValueError, dyn_mimo.__radd__, dyn_mimo_sq)
assert_raises(ValueError, dyn_mimo.__rsub__, dyn_mimo_sq)
def test_e_i():
assert_almost_equal(e_i(7, 5, output='r'),
array([[0., 0., 0., 0., 0., 1., 0.]])
)
assert_almost_equal(e_i(5, [0, 4, 4, 4, 1]),
array([[1., 0., 0., 0., 0.],
[0., 0., 0., 0., 1.],
[0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.],
[0., 1., 1., 1., 0.]])
)
assert_almost_equal(e_i(5, s_[1:3]),
array([[0., 0.],
[1., 0.],
[0., 1.],
[0., 0.],
[0., 0.]])
)
assert_almost_equal(e_i(5, slice(1, 5, 2), output='r'),
array([[0., 1., 0., 0., 0.],
[0., 0., 0., 1., 0.]])
)
def test_State_algebra_add_radd():
sta_siso = State(5)
sta_mimo = State(2.0*np.eye(3))
dyn_siso = State(haroldcompanion([1, 3, 3, 1]), e_i(3, -1), e_i(3, 1).T)
dyn_mimo = State(haroldcompanion([1, 3, 3, 1]), e_i(3, [1, 2]), np.eye(3))
dyn_mimo_sq = State(haroldcompanion([1, 3, 3, 1]), np.eye(3), np.eye(3))
G = dyn_mimo + sta_siso
assert_array_almost_equal(G.d, sta_siso.to_array()*np.ones(dyn_mimo.shape))
assert_raises(ValueError, dyn_mimo.__add__, sta_mimo)
G = dyn_mimo_sq + sta_mimo
assert_array_almost_equal(G.d, 2.*np.eye(3))
G = dyn_mimo + dyn_siso
J = np.array([[0., 1., 0., 0., 0., 0., 0., 0.],
[0., 0., 1., 0., 0., 0., 1., 0.],
[-1., -3., -3., 0., 0., 0., 0., 1.],
[0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., -1., -3., -3., 1., 1.],
[1., 0., 0., 0., 1., 0., 0., 0.],
[0., 1., 0., 0., 1., 0., 0., 0.],
[0., 0., 1., 0., 1., 0., 0., 0.]])
assert_array_almost_equal(concatenate_state_matrices(G), J)
assert_raises(ValueError, dyn_mimo.__add__, dyn_mimo_sq)
assert_raises(ValueError, dyn_mimo.__sub__, dyn_mimo_sq)
assert_raises(ValueError, dyn_mimo.__radd__, dyn_mimo_sq)
assert_raises(ValueError, dyn_mimo.__rsub__, dyn_mimo_sq)
def test_e_i():
assert_almost_equal(e_i(7, 5, output='r'),
array([[0., 0., 0., 0., 0., 1., 0.]]))
assert_almost_equal(
e_i(5, [0, 4, 4, 4, 1]),
array([[1., 0., 0., 0., 0.], [0., 0., 0., 0.,
1.], [0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0.], [0., 1., 1., 1., 0.]]))
assert_almost_equal(
e_i(5, s_[1:3]),
array([[0., 0.], [1., 0.], [0., 1.], [0., 0.], [0., 0.]]))
assert_almost_equal(e_i(5, slice(1, 5, 2), output='r'),
array([[0., 1., 0., 0., 0.], [0., 0., 0., 1., 0.]]))
def test_State_algebra_mul_rmul_mimo_siso():
sta_siso = State(5)
sta_mimo = State(2.0*np.eye(3))
dyn_siso = State(haroldcompanion([1, 3, 3, 1]), e_i(3, -1), e_i(3, 1).T)
dyn_mimo = State(haroldcompanion([1, 3, 3, 1]), e_i(3, [1, 2]), np.eye(3))
dyn_mimo_sq = State(haroldcompanion([1, 3, 3, 1]), np.eye(3), np.eye(3))
G = dyn_siso * dyn_mimo
J = np.array([[0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 1., 0., 1., 0., 0., 0., 0., 0., 0.],
[-1., -3., -3., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
[0., 0., 0., -1., -3., -3., 0., 0., 0., 1., 0.],
[0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0.],
[0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.],
[0., 0., 0., 0., 0., 0., -1., -3., -3., 0., 1.],
[1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.]])
assert_array_almost_equal(concatenate_state_matrices(G), J)
G = dyn_mimo * dyn_siso
assert_array_almost_equal(concatenate_state_matrices(G), J)
G = dyn_mimo * sta_siso
assert_array_almost_equal(G.b, 5*dyn_mimo.b)
assert_array_almost_equal(G.d, 5*dyn_mimo.d)
assert_raises(ValueError, sta_mimo.__add__, dyn_mimo)
F = sta_mimo @ dyn_mimo
J = np.array([[0., 1., 0., 0., 0.],
[0., 0., 1., 1., 0.],
[-1., -3., -3., 0., 1.],
[2., 0., 0., 0., 0.],
[0., 2., 0., 0., 0.],
[0., 0., 2., 0., 0.]])
assert_array_almost_equal(concatenate_state_matrices(F), J)
assert_almost_equal((dyn_mimo_sq + sta_mimo).d, 2*np.eye(3))
def test_model_zeros():
# Test example
A = np.array([
[-3.93, -0.00315, 0, 0, 0, 4.03E-5, 0, 0, 0],
[368, -3.05, 3.03, 0, 0, -3.77E-3, 0, 0, 0],
[27.4, 0.0787, -5.96E-2, 0, 0, -2.81E-4, 0, 0, 0],
[-0.0647, -5.2E-5, 0, -0.255, -3.35E-6, 3.6e-7, 6.33E-5, 1.94E-4, 0],
[3850, 17.3, -12.8, -12600, -2.91, -0.105, 12.7, 43.1, 0],
[22400, 18, 0, -35.6, -1.04E-4, -0.414, 90, 56.9, 0],
[0, 0, 2.34E-3, 0, 0, 2.22E-4, -0.203, 0, 0],
[0, 0, 0, -1.27, -1.00E-3, 7.86E-5, 0, -7.17E-2, 0],
[-2.2, -177e-5, 0, -8.44, -1.11E-4, 1.38E-5, 1.49E-3, 6.02E-3, -1E-10]
])
B = np.array([[0, 0], [0, 0], [1.56, 0], [0, -5.13E-6], [8.28, -1.55],
[0, 1.78], [2.33, 0], [0, -2.45E-2], [0, 2.94E-5]])
C = e_i(9, [5, 8], output='r')
D = np.zeros((2, 2))
zs = transmission_zeros(A, B, C, D)
res = np.array([
-2.64128629e+01 - 0j, -2.93193619 - 0.419522621j, -9.52183370e-03 + 0j,
-2.93193619 + 0.419522621j, 1.69789270e-01 - 0j, 5.46527700e-01 - 0j
])
# Sort is numerically too sensitive for imaginary parts.
assert_almost_equal(np.sort(np.imag(zs)), np.sort(np.imag(res))) # 0.0
assert_almost_equal(np.sort(np.real(zs)), np.sort(np.real(res))) # 0.1
# An example found online (citation lost), please let me know
A = np.array([[-6.5000, 0.5000, 6.5000, -6.5000],
[-0.5000, -5.5000, -5.5000, 5.5000],
[-0.5000, 0.5000, 0.5000, -6.5000],
[-0.5000, 0.5000, -5.5000, -0.5000]])
B = np.array([[0., 1, 0], [2., 1, 2], [3., 4, 3], [3., 2, 3]])
C = np.array([[1, 1, 0, 0]])
D = np.zeros((1, 3))
zs = transmission_zeros(A, B, C, D)
res = np.array([-7, -6])
assert_almost_equal(np.sort(res), np.sort(zs)) # 1
# Example from Reinschke, 1988
A = np.array([[0, 0, 1, 0, 0, 0], [2, 0, 0, 3, 4, 0], [0, 0, 5, 0, 0, 6],
[0, 7, 0, 0, 0, 0], [0, 0, 0, 8, 9, 0], [0, 0, 0, 0, 0, 0]])
B = np.array([[0, 0, 0, 0, 10, 0], [0, 0, 0, 0, 0, 11]]).T
C = np.array([[0, 12, 0, 0, 13, 0], [14, 0, 0, 0, 0, 0],
[15, 0, 16, 0, 0, 0]])
D = np.zeros((3, 2))
zs = transmission_zeros(A, B, C, D)
res = np.array([-6.78662791 + 0.j, 3.09432022 + 0.j])
assert_almost_equal(np.sort(zs), np.sort(res)) # 2
def test_model_zeros():
# Test example
A = np.array(
[[-3.93, -0.00315, 0, 0, 0, 4.03E-5, 0, 0, 0],
[368, -3.05, 3.03, 0, 0, -3.77E-3, 0, 0, 0],
[27.4, 0.0787, -5.96E-2, 0, 0, -2.81E-4, 0, 0, 0],
[-0.0647, -5.2E-5, 0, -0.255, -3.35E-6, 3.6e-7, 6.33E-5, 1.94E-4, 0],
[3850, 17.3, -12.8, -12600, -2.91, -0.105, 12.7, 43.1, 0],
[22400, 18, 0, -35.6, -1.04E-4, -0.414, 90, 56.9, 0],
[0, 0, 2.34E-3, 0, 0, 2.22E-4, -0.203, 0, 0],
[0, 0, 0, -1.27, -1.00E-3, 7.86E-5, 0, -7.17E-2, 0],
[-2.2, -177e-5, 0, -8.44, -1.11E-4, 1.38E-5, 1.49E-3, 6.02E-3, -1E-10]
])
B = np.array([[0, 0],
[0, 0],
[1.56, 0],
[0, -5.13E-6],
[8.28, -1.55],
[0, 1.78],
[2.33, 0],
[0, -2.45E-2],
[0, 2.94E-5]
])
C = e_i(9, [5, 8], output='r')
D = np.zeros((2, 2))
zs = transmission_zeros(A, B, C, D)
res = np.array([-2.64128629e+01 - 0j,
-2.93193619 - 0.419522621j,
-9.52183370e-03 + 0j,
-2.93193619 + 0.419522621j,
1.69789270e-01 - 0j,
5.46527700e-01 - 0j])
# Sort is numerically too sensitive for imaginary parts.
assert_almost_equal(np.sort(np.imag(zs)), np.sort(np.imag(res))) # 0.0
assert_almost_equal(np.sort(np.real(zs)), np.sort(np.real(res))) # 0.1
# An example found online (citation lost), please let me know
A = np.array([[-6.5000, 0.5000, 6.5000, -6.5000],
[-0.5000, -5.5000, -5.5000, 5.5000],
[-0.5000, 0.5000, 0.5000, -6.5000],
[-0.5000, 0.5000, -5.5000, -0.5000]])
B = np.array([[0., 1, 0],
[2., 1, 2],
[3., 4, 3],
[3., 2, 3]])
C = np.array([[1, 1, 0, 0]])
D = np.zeros((1, 3))
zs = transmission_zeros(A, B, C, D)
res = np.array([-7, -6])
assert_almost_equal(np.sort(res), np.sort(zs)) # 1
# Example from Reinschke, 1988
A = np.array([[0, 0, 1, 0, 0, 0],
[2, 0, 0, 3, 4, 0],
[0, 0, 5, 0, 0, 6],
[0, 7, 0, 0, 0, 0],
[0, 0, 0, 8, 9, 0],
[0, 0, 0, 0, 0, 0]])
B = np.array([[0, 0, 0, 0, 10, 0], [0, 0, 0, 0, 0, 11]]).T
C = np.array([[0, 12, 0, 0, 13, 0],
[14, 0, 0, 0, 0, 0],
[15, 0, 16, 0, 0, 0]])
D = np.zeros((3, 2))
zs = transmission_zeros(A, B, C, D)
res = np.array([-6.78662791+0.j, 3.09432022+0.j])
assert_almost_equal(np.sort(zs), np.sort(res)) # 2
