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_matmul_rmatmul_ndarray():
H = State([[-5, -2], [1, 0]], [[2], [0]], [3, 1], 1)
J1 = np.array([[-5., -2., 0., 0., 0., 0., 2., 4., 6., 8.],
[1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., -5., -2., 0., 0., 10., 12., 14., 16.],
[0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., -5., -2., 18., 20., 22., 24.],
[0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
[3., 1., 0., 0., 0., 0., 1., 2., 3., 4.],
[0., 0., 3., 1., 0., 0., 5., 6., 7., 8.],
[0., 0., 0., 0., 3., 1., 9., 10., 11., 12.]])
J2 = np.array([[-5., -2., 0., 0., 0., 0., 2., 0., 0.],
[1., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., -5., -2., 0., 0., 0., 2., 0.],
[0., 0., 1., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., -5., -2., 0., 0., 2.],
[0., 0., 0., 0., 1., 0., 0., 0., 0.],
[3., 1., 6., 2., 9., 3., 1., 2., 3.],
[12., 4., 15., 5., 18., 6., 4., 5., 6.],
[21., 7., 24., 8., 27., 9., 7., 8., 9.],
[30., 10., 33., 11., 36., 12., 10., 11., 12.]])
mat = np.arange(1, 13).reshape(3, 4)
Fm = concatenate_state_matrices(mat @ H)
assert_array_almost_equal(J1, Fm)
Fm = concatenate_state_matrices(H @ mat)
assert_array_almost_equal(J1, Fm)
mat = np.arange(1, 13).reshape(4, 3)
Fm = concatenate_state_matrices(mat @ H)
assert_array_almost_equal(J2, Fm)
Fm = concatenate_state_matrices(H @ mat)
assert_array_almost_equal(J2, Fm)
def test_State_slicing():
F = State(1, 2, 3, 4)
F0 = F[0, 0]
assert_equal(concatenate_state_matrices(F), concatenate_state_matrices(F0))
F = State(np.random.rand(4, 4))
H = State(F.d, np.random.rand(4, 3), np.random.rand(5, 4))
Hind = [(1, 3), (5, 1),
(5, 3), (1, 1),
(2, 3), (5, 2),
(2, 3), (5, 2),
(1, 2), (2, 1),
(3, 3), (5, 2)]
Find = [(1, 4), (4, 1),
(4, 4), (1, 1),
(2, 4), (4, 2),
(2, 4), (4, 2),
(1, 2), (2, 1),
(2, 4), (4, 2)]
for s, sind in ((H, Hind), (F, Find)):
for ind, x in enumerate([s[1, :], s[:, 1],
s[:, :], s[0, 0],
s[1:3, :], s[:, 1:3],
s[[1, 2], :], s[:, [1, 2]],
s[2, [1, 2]], s[[1, 2], 2],
s[::2, :], s[:, ::2]]):
assert_equal(x.shape, sind[ind])
assert_raises(ValueError, H.__setitem__)
def test_transfer_to_state():
# Models with static column/row
num, den = [[1, -1], [[1, -1], 0]], [[[1, 2], 1], [[1, 2], 1]]
den2, num2 = [list(i) for i in zip(*den)], [list(i) for i in zip(*num)]
G = Transfer(num, den)
H = Transfer(num2, den2)
Gs = transfer_to_state(G)
Hs = transfer_to_state(H)
Gm = concatenate_state_matrices(Gs)
Hm = concatenate_state_matrices(Hs)
assert_array_almost_equal(Gm, np.array([[-2, 1, 0], [1, 0, -1], [-3, 1,
0]]))
assert_array_almost_equal(
Hm,
np.array([[-2., 0., 1., 0.], [0., -2., 0., 1.], [1., -3., 0., 1.],
[0., 0., -1., 0.]]))
# Example from Kalman 1963
num = [[3 * np.poly([-3, -5]), [6, 6], [2, 7], [2, 5]],
[2, 1, [2, 10], [8, 16]],
[[2, 14, 36], [-2, 0], 1, 2 * np.convolve([5, 17], [1, 2])]]
den = [[np.poly([-1, -2, -4]), [1, 6, 8], [1, 7, 12], [1, 5, 6]],
[[1, 8, 15], [1, 3],
np.poly([-1, -2, -3]),
np.poly([-1, -3, -5])],
[np.poly([-1, -3, -5]), [1, 4, 3], [1, 3],
np.poly([-1, -3, -5])]]
G = Transfer(num, den)
H = transfer_to_state(G)
p = H.poles
p.sort()
assert_array_almost_equal(
p,
np.array([
-5. + 0.j, -5. + 0.j, -4. + 0.j, -3. + 0.j, -3. + 0.j, -3. + 0.j,
-2. + 0.j, -2. + 0.j, -1. + 0.j, -1. + 0.j, -1. + 0.j
]))
# Reported in gh-#42
G = Transfer([[[87.8, 8.78], [-103.68, -8.64]],
[[129.84, 10.82], [-109.6, -10.96]]], [562.5, 82.5, 1])
Gss = transfer_to_state(G)
assert_array_almost_equal(
Gss.a, np.kron(np.eye(2), [[0., 1.], [-2 / 1125, -11 / 75]]))
assert_array_almost_equal(Gss.b, [[0, 0], [1, 0], [0, 0], [0, 1]])
des_c = np.array([[
0.01560888888888889, 0.1560888888888889, -0.015360000000000002,
-0.18432
],
[
0.019235555555555558, 0.23082666666666668,
-0.019484444444444447, -0.19484444444444443
]])
assert_array_almost_equal(Gss.c, des_c)
assert_array_almost_equal(Gss.d, np.zeros([2, 2]))
def test_State_algebra_mul_rmul_scalar_array():
G = State(np.diag([-1, -2]), [[1, 2], [3, 4]], np.eye(2))
F = G * np.eye(2)
Fm = G @ np.eye(2)
assert_equal(concatenate_state_matrices(F), concatenate_state_matrices(Fm))
F = np.eye(2) * G
Fm = np.eye(2) @ G
assert_equal(concatenate_state_matrices(F), concatenate_state_matrices(Fm))
H = 1 / 2 * G
assert_equal(H.c, 0.5 * G.c)
def test_State_algebra_mul_rmul_scalar_array():
G = State(np.diag([-1, -2]), [[1, 2], [3, 4]], np.eye(2))
F = G*np.eye(2)
Fm = [email protected](2)
assert_equal(concatenate_state_matrices(F), concatenate_state_matrices(Fm))
F = np.eye(2)*G
Fm = np.eye(2)@G
assert_equal(concatenate_state_matrices(F), concatenate_state_matrices(Fm))
H = 1/2*G
assert_equal(H.c, 0.5*G.c)
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_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_transfer_to_state():
# Models with static column/row
num, den = [[1, -1], [[1, -1], 0]], [[[1, 2], 1], [[1, 2], 1]]
den2, num2 = [list(i) for i in zip(*den)], [list(i) for i in zip(*num)]
G = Transfer(num, den)
H = Transfer(num2, den2)
Gs = transfer_to_state(G)
Hs = transfer_to_state(H)
Gm = concatenate_state_matrices(Gs)
Hm = concatenate_state_matrices(Hs)
assert_array_almost_equal(Gm, np.array([[-2, 1, 0], [1, 0, -1], [-3, 1,
0]]))
assert_array_almost_equal(
Hm,
np.array([[-2., 0., 1., 0.], [0., -2., 0., 1.], [1., -3., 0., 1.],
[0., 0., -1., 0.]]))
# Example from Kalman 1963
num = [[3 * np.poly([-3, -5]), [6, 6], [2, 7], [2, 5]],
[2, 1, [2, 10], [8, 16]],
[[2, 14, 36], [-2, 0], 1, 2 * np.convolve([5, 17], [1, 2])]]
den = [[np.poly([-1, -2, -4]), [1, 6, 8], [1, 7, 12], [1, 5, 6]],
[[1, 8, 15], [1, 3],
np.poly([-1, -2, -3]),
np.poly([-1, -3, -5])],
[np.poly([-1, -3, -5]), [1, 4, 3], [1, 3],
np.poly([-1, -3, -5])]]
G = Transfer(num, den)
H = transfer_to_state(G)
p = H.poles
p.sort()
assert_array_almost_equal(
p,
np.array([
-5. + 0.j, -5. + 0.j, -4. + 0.j, -3. + 0.j, -3. + 0.j, -3. + 0.j,
-2. + 0.j, -2. + 0.j, -1. + 0.j, -1. + 0.j, -1. + 0.j
]))
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_feedback_dynamic_static():
M = array([[2, 2, 1, -1],
[3, 2, -2, 3],
[1, -1, 1, -3],
[0, -1, 2, 0]])
a, b, c, d = matrix_slice(M, [3, 3])
G = State(a, b, eye(3))
H, _, _ = lqr(G, eye(3))
CL = feedback(G, H)
assert_almost_equal(CL.poles,
array([-5.42998305, -3.75504185, -1.55400925]))
G = State(a, b, c, d)
CL = feedback(G, 5+0j)
assert_almost_equal(concatenate_state_matrices(CL),
array([[2., -3., 11., -1.],
[3., 17., -32., 3.],
[1., -16., 31., -3.],
[0., -1., 2., 0.]]))
CL = feedback(5, G)
assert_almost_equal(concatenate_state_matrices(CL),
array([[2., -3., 11., -5.],
[3., 17., -32., 15.],
[1., -16., 31., -15.],
[0., 5., -10., 5.]]))
def test_State_matmul_rmatmul_ndarray():
H = State([[-5, -2], [1, 0]], [[2], [0]], [3, 1], 1)
J1 = np.array([[-5., -2., 0., 0., 0., 0., 2., 4., 6., 8.],
[1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., -5., -2., 0., 0., 10., 12., 14., 16.],
[0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., -5., -2., 18., 20., 22., 24.],
[0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
[3., 1., 0., 0., 0., 0., 1., 2., 3., 4.],
[0., 0., 3., 1., 0., 0., 5., 6., 7., 8.],
[0., 0., 0., 0., 3., 1., 9., 10., 11., 12.]])
J2 = np.array([[-5., -2., 0., 0., 0., 0., 2., 0., 0.],
[1., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., -5., -2., 0., 0., 0., 2., 0.],
[0., 0., 1., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., -5., -2., 0., 0., 2.],
[0., 0., 0., 0., 1., 0., 0., 0., 0.],
[3., 1., 6., 2., 9., 3., 1., 2., 3.],
[12., 4., 15., 5., 18., 6., 4., 5., 6.],
[21., 7., 24., 8., 27., 9., 7., 8., 9.],
[30., 10., 33., 11., 36., 12., 10., 11., 12.]])
mat = np.arange(1, 13).reshape(3, 4)
Fm = concatenate_state_matrices(mat @ H)
assert_array_almost_equal(J1, Fm)
Fm = concatenate_state_matrices(H @ mat)
assert_array_almost_equal(J1, Fm)
mat = np.arange(1, 13).reshape(4, 3)
Fm = concatenate_state_matrices(mat @ H)
assert_array_almost_equal(J2, Fm)
Fm = concatenate_state_matrices(H @ mat)
assert_array_almost_equal(J2, Fm)
G, H = random_state_model(2, 2, 2), random_state_model(2, 3, 3)
with assert_raises(ValueError):
G @ H
# Scalars
G = random_state_model(1)
H = 0. @ G
assert H._isgain
H = 1. @ G
assert_almost_equal(concatenate_state_matrices(G),
concatenate_state_matrices(H))
# static gain mults
G = random_state_model(0, 4, 5)
H = random_state_model(0, 5, 4)
assert (G @ H)._isgain
assert_equal((G @ H).shape, (4, 4))
H = random_state_model(0, 3, 3)
with assert_raises(ValueError):
G @ H
G = State(1.)
H = random_state_model(1, 2, 2)
assert_almost_equal(concatenate_state_matrices(G @ H),
concatenate_state_matrices(H @ G))
G = random_state_model(1, 4, 5)
H = random_state_model(1, 4, 5)
with assert_raises(ValueError):
G @ H
def test_transfer_to_state():
# Models with static column/row
num, den = [[1, -1], [[1, -1], 0]], [[[1, 2], 1], [[1, 2], 1]]
den2, num2 = [list(i) for i in zip(*den)], [list(i) for i in zip(*num)]
G = Transfer(num, den)
H = Transfer(num2, den2)
Gs = transfer_to_state(G)
Hs = transfer_to_state(H)
Gm = concatenate_state_matrices(Gs)
Hm = concatenate_state_matrices(Hs)
assert_array_almost_equal(Gm, np.array([[-2, 1, 0], [1, 0, -1], [-3, 1,
0]]))
assert_array_almost_equal(
Hm,
np.array([[-2., 0., 1., 0.], [0., -2., 0., 1.], [1., -3., 0., 1.],
[0., 0., -1., 0.]]))
# Example from Kalman 1963
num = [[3 * np.poly([-3, -5]), [6, 6], [2, 7], [2, 5]],
[2, 1, [2, 10], [8, 16]],
[[2, 14, 36], [-2, 0], 1, 2 * np.convolve([5, 17], [1, 2])]]
den = [[np.poly([-1, -2, -4]), [1, 6, 8], [1, 7, 12], [1, 5, 6]],
[[1, 8, 15], [1, 3],
np.poly([-1, -2, -3]),
np.poly([-1, -3, -5])],
[np.poly([-1, -3, -5]), [1, 4, 3], [1, 3],
np.poly([-1, -3, -5])]]
G = Transfer(num, den)
H = transfer_to_state(G)
p = H.poles
p.sort()
assert_array_almost_equal(
p,
np.array([
-5. + 0.j, -5. + 0.j, -4. + 0.j, -3. + 0.j, -3. + 0.j, -3. + 0.j,
-2. + 0.j, -2. + 0.j, -1. + 0.j, -1. + 0.j, -1. + 0.j
]))
# Reported in gh-#42
G = Transfer([[[87.8, 8.78], [-103.68, -8.64]],
[[129.84, 10.82], [-109.6, -10.96]]], [562.5, 82.5, 1])
Gss = transfer_to_state(G)
assert_array_almost_equal(
Gss.a, np.kron(np.eye(2), [[0., 1.], [-2 / 1125, -11 / 75]]))
assert_array_almost_equal(Gss.b, [[0, 0], [1, 0], [0, 0], [0, 1]])
des_c = np.array([[
0.01560888888888889, 0.1560888888888889, -0.015360000000000002,
-0.18432
],
[
0.019235555555555558, 0.23082666666666668,
-0.019484444444444447, -0.19484444444444443
]])
assert_array_almost_equal(Gss.c, des_c)
assert_array_almost_equal(Gss.d, np.zeros([2, 2]))
# reported in gh-#50
num = [[[61.79732492202783, 36.24988430260625, 0.7301196233698941],
[0.0377840674057878, 0.9974993795127982, 21.763622825733773]]]
den = [[[84.64, 18.4, 1.0], [1.0, 7.2, 144.0]]]
TF = transfer_to_state((num, den))
assert_array_almost_equal([
-3.6 - 1.14472704e+01j,
-3.6 + 1.14472704e+01j,
-0.10869565 - 1.74405237e-07j,
-0.10869565 + 1.74405237e-07j,
], np.sort(TF.poles))
assert TF.zeros.size == 0
# rectengular static gain
gain = np.ones([2, 3])
Gss = transfer_to_state(Transfer(gain))
assert_array_almost_equal(gain, Gss.d)
def test_transfer_to_state():
# Models with static column/row
num, den = [[1, -1], [[1, -1], 0]], [[[1, 2], 1], [[1, 2], 1]]
den2, num2 = [list(i) for i in zip(*den)], [list(i) for i in zip(*num)]
G = Transfer(num, den)
H = Transfer(num2, den2)
Gs = transfer_to_state(G)
Hs = transfer_to_state(H)
Gm = concatenate_state_matrices(Gs)
Hm = concatenate_state_matrices(Hs)
assert_array_almost_equal(Gm, np.array([[-2, 1, 0],
[1, 0, -1],
[-3, 1, 0]]))
assert_array_almost_equal(Hm, np.array([[-2., 0., 1., 0.],
[0., -2., 0., 1.],
[1., -3., 0., 1.],
[0., 0., -1., 0.]]))
# Example from Kalman 1963
num = [[3*np.poly([-3, -5]), [6, 6], [2, 7], [2, 5]],
[2, 1, [2, 10], [8, 16]],
[[2, 14, 36], [-2, 0], 1, 2*np.convolve([5, 17], [1, 2])]]
den = [[np.poly([-1, -2, -4]), [1, 6, 8], [1, 7, 12], [1, 5, 6]],
[[1, 8, 15], [1, 3], np.poly([-1, -2, -3]), np.poly([-1, -3, -5])],
[np.poly([-1, -3, -5]), [1, 4, 3], [1, 3], np.poly([-1, -3, -5])]]
G = Transfer(num, den)
H = transfer_to_state(G)
p = H.poles
p.sort()
assert_array_almost_equal(p, np.array([-5.+0.j, -5.+0.j, -4.+0.j,
-3.+0.j, -3.+0.j, -3.+0.j,
-2.+0.j, -2.+0.j, -1.+0.j,
-1.+0.j, -1.+0.j]))
# Reported in gh-#42
G = Transfer([[[87.8, 8.78], [-103.68, -8.64]],
[[129.84, 10.82], [-109.6, -10.96]]],
[562.5, 82.5, 1])
Gss = transfer_to_state(G)
assert_array_almost_equal(Gss.a, np.kron(np.eye(2), [[0., 1.],
[-2/1125, -11/75]]))
assert_array_almost_equal(Gss.b, [[0, 0], [1, 0], [0, 0], [0, 1]])
des_c = np.array([[0.01560888888888889,
0.1560888888888889,
-0.015360000000000002,
-0.18432],
[0.019235555555555558,
0.23082666666666668,
-0.019484444444444447,
-0.19484444444444443]])
assert_array_almost_equal(Gss.c, des_c)
assert_array_almost_equal(Gss.d, np.zeros([2, 2]))
# reported in gh-#50
num = [[[61.79732492202783, 36.24988430260625, 0.7301196233698941],
[0.0377840674057878, 0.9974993795127982, 21.763622825733773]]]
den = [[[84.64, 18.4, 1.0], [1.0, 7.2, 144.0]]]
TF = transfer_to_state((num, den))
assert_array_almost_equal([-3.6-1.14472704e+01j,
-3.6+1.14472704e+01j,
-0.10869565-1.74405237e-07j,
-0.10869565+1.74405237e-07j,
],
np.sort(TF.poles))
assert TF.zeros.size == 0
def test_State_matmul_rmatmul_ndarray():
H = State([[-5, -2], [1, 0]], [[2], [0]], [3, 1], 1)
J1 = np.array([[-5., -2., 0., 0., 0., 0., 2., 4., 6., 8.],
[1., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., -5., -2., 0., 0., 10., 12., 14., 16.],
[0., 0., 1., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., -5., -2., 18., 20., 22., 24.],
[0., 0., 0., 0., 1., 0., 0., 0., 0., 0.],
[3., 1., 0., 0., 0., 0., 1., 2., 3., 4.],
[0., 0., 3., 1., 0., 0., 5., 6., 7., 8.],
[0., 0., 0., 0., 3., 1., 9., 10., 11., 12.]])
J2 = np.array([[-5., -2., 0., 0., 0., 0., 2., 0., 0.],
[1., 0., 0., 0., 0., 0., 0., 0., 0.],
[0., 0., -5., -2., 0., 0., 0., 2., 0.],
[0., 0., 1., 0., 0., 0., 0., 0., 0.],
[0., 0., 0., 0., -5., -2., 0., 0., 2.],
[0., 0., 0., 0., 1., 0., 0., 0., 0.],
[3., 1., 6., 2., 9., 3., 1., 2., 3.],
[12., 4., 15., 5., 18., 6., 4., 5., 6.],
[21., 7., 24., 8., 27., 9., 7., 8., 9.],
[30., 10., 33., 11., 36., 12., 10., 11., 12.]])
mat = np.arange(1, 13).reshape(3, 4)
Fm = concatenate_state_matrices(mat @ H)
assert_array_almost_equal(J1, Fm)
Fm = concatenate_state_matrices(H @ mat)
assert_array_almost_equal(J1, Fm)
mat = np.arange(1, 13).reshape(4, 3)
Fm = concatenate_state_matrices(mat @ H)
assert_array_almost_equal(J2, Fm)
Fm = concatenate_state_matrices(H @ mat)
assert_array_almost_equal(J2, Fm)
G, H = random_state_model(2, 2, 2), random_state_model(2, 3, 3)
with assert_raises(ValueError):
G @ H
# Scalars
G = random_state_model(1)
H = 0. @ G
assert H._isgain
H = 1. @ G
assert_almost_equal(concatenate_state_matrices(G),
concatenate_state_matrices(H))
# static gain mults
G = random_state_model(0, 4, 5)
H = random_state_model(0, 5, 4)
assert (G@H)._isgain
assert_equal((G@H).shape, (4, 4))
H = random_state_model(0, 3, 3)
with assert_raises(ValueError):
G @ H
G = State(1.)
H = random_state_model(1, 2, 2)
assert_almost_equal(concatenate_state_matrices(G @ H),
concatenate_state_matrices(H @ G))
G = random_state_model(1, 4, 5)
H = random_state_model(1, 4, 5)
with assert_raises(ValueError):
G @ H
def test_concatenate_state_matrices():
G = State(1, 2, 3, 4)
M = concatenate_state_matrices(G)
assert_array_equal(M, np.array([[1, 2], [3, 4]])) # 1
G = State(np.eye(4))
assert_array_equal(concatenate_state_matrices(G), np.eye(4))
def test_concatenate_state_matrices():
G = State(1, 2, 3, 4)
M = concatenate_state_matrices(G)
assert_array_equal(M, np.array([[1, 2], [3, 4]])) # 1
G = State(np.eye(4))
assert_array_equal(concatenate_state_matrices(G), np.eye(4))
