def test_Ny2_Nu2(i, j, zero_Pzw=True, Ts=0.008):
""" Correct impulse response for y in R and u in R.
"""
P = random_dtime_sys(5, 5, Ts)
Pzw, Pzu, Pyw, Pyu = Ss.get_partitioned_transfer_matrices(P, 2, 2)
if zero_Pzw:
Pzw = Ss.tf_blocks(np.zeros((3, 3)), dt=Ts)
weight = np.random.randn(12)
# weight = np.array([0, 0, 0., 1., 0.0, 0.0]) # for debug
freqs = np.linspace(0, 100, 50)
z = co.tf([1, 0], [1], Ts)
Q00 = Ts * (weight[0] + weight[1] * z**(-1) + weight[2] * z**(-2))
Q01 = Ts * (weight[3] + weight[4] * z**(-1) + weight[5] * z**(-2))
Q10 = Ts * (weight[6] + weight[7] * z**(-1) + weight[8] * z**(-2))
Q11 = Ts * (weight[9] + weight[10] * z**(-1) + weight[11] * z**(-2))
# expected result
H_expected = Pzw[i, j] + (
Pzu[i, 0] * Q00 * Pyw[0, j] + Pzu[i, 0] * Q01 * Pyw[1, j] +
Pzu[i, 1] * Q10 * Pyw[0, j] + Pzu[i, 1] * Q11 * Pyw[1, j])
mag, phase, _ = H_expected.freqresp(freqs)
fresp_expected = mag[0, 0] * np.exp(1j * phase[0, 0])
# actual result
fresp_actual = Ss.Qsyn.obtain_freq_var(weight, (i, j), freqs, Pzw, Pzu,
Pyw)
# # # debug plot
# plt.plot(np.abs(fresp_actual))
# plt.plot(np.abs(fresp_expected), '--')
# plt.show()
np.testing.assert_allclose(fresp_expected, fresp_actual, atol=1e-5)
def test_Ny1_Nu1(i, j, Ts=0.008):
""" Correct impulse response for y in R and u in R.
"""
P = random_dtime_sys(5, 5, Ts)
Pzw, Pzu, Pyw, Pyu = Ss.get_partitioned_transfer_matrices(P, 1, 1)
weight = np.array([0.1, 0.4, 0, 0.2])
freqs = np.linspace(0, 100, 50)
z = co.tf([1, 0], [1], Ts)
Q = Ts * (0.1 + 0.4 * z**(-1) + 0 + 0.2 * z**(-3))
# expected result
H_expected = Pzw[i, j] + Pzu[i, 0] * Q * Pyw[0, j]
mag, phase, _ = H_expected.freqresp(freqs)
fresp_expected = mag[0, 0] * np.exp(1j * phase[0, 0])
# actual result
fresp_actual = Ss.Qsyn.obtain_freq_var(weight, (i, j), freqs, Pzw, Pzu,
Pyw)
# # # debug plot
# plt.plot(np.abs(fresp_actual))
# plt.plot(np.abs(fresp_expected), '--')
# plt.show()
np.testing.assert_allclose(fresp_expected, fresp_actual, atol=1e-5)
def test_Ny2_Nu2(i, j, zero_Pzw=True, Ts=0.008):
""" Correct impulse response for y in R and u in R.
"""
P = random_dtime_sys(5, 5, Ts)
Pzw, Pzu, Pyw, Pyu = Ss.get_partitioned_transfer_matrices(P, 2, 2)
if zero_Pzw:
Pzw = Ss.tf_blocks(np.zeros((3, 3)), dt=Ts)
weight = np.random.randn(12)
# weight = np.array([0, 0, 0., 1., 0.0, 0.0]) # for debug
Tsim = np.arange(30) * Ts
z = co.tf([1, 0], [1], Ts)
Q00 = Ts * (weight[0] + weight[1] * z ** (-1) + weight[2] * z ** (-2))
Q01 = Ts * (weight[3] + weight[4] * z ** (-1) + weight[5] * z ** (-2))
Q10 = Ts * (weight[6] + weight[7] * z ** (-1) + weight[8] * z ** (-2))
Q11 = Ts * (weight[9] + weight[10] * z ** (-1) + weight[11] * z ** (-2))
# expected result
H_expected = Pzw[i, j] + (Pzu[i, 0] * Q00 * Pyw[0, j]
+ Pzu[i, 0] * Q01 * Pyw[1, j]
+ Pzu[i, 1] * Q10 * Pyw[0, j]
+ Pzu[i, 1] * Q11 * Pyw[1, j])
_, imp_expected = co.impulse_response(H_expected, Tsim)
imp_expected = imp_expected[0, :]
# actual result
imp_actual = Ss.Qsyn.obtain_time_response_var(weight, (i, j), Tsim, Pzw, Pzu, Pyw)
# # debug plot
# plt.plot(imp_actual)
# plt.plot(imp_expected, '--')
# plt.show()
np.testing.assert_allclose(imp_expected, imp_actual, atol=1e-8)
def test_wrong_Tsim():
""" Given sim Time has wrong increment.
"""
P = random_dtime_sys(2, 2, 0.008)
Pzw, Pzu, Pyw, Pyu = Ss.get_partitioned_transfer_matrices(P, 1, 1)
with pytest.raises(ValueError) as exinfo:
Ss.Qsyn.obtain_time_response_var([0, 1, 2, 3], (0, 0), np.arange(5), Pzw, Pzu, Pyw)
assert str(exinfo.value) == "Inconsistent simulation time `Tsim`"
def test_wrong_weight_dim():
""" Given weight have wrong dimension.
"""
P = random_dtime_sys(5, 5, 0.008)
Pzw, Pzu, Pyw, Pyu = Ss.get_partitioned_transfer_matrices(P, 2, 3)
weight = np.random.randn(11) # 11 = 6 + 5
Tsim = np.arange(100) * 0.008
with pytest.raises(ValueError) as exinfo:
Ss.Qsyn.obtain_time_response_var(weight, (0, 0), Tsim, Pzw, Pzu, Pyw)
assert str(exinfo.value) == "Inconsistent weight dimension"
def test_Ny1_Nu1(i, j, Ts=0.008):
""" Correct impulse response for y in R and u in R.
"""
P = random_dtime_sys(5, 5, Ts)
Pzw, Pzu, Pyw, Pyu = Ss.get_partitioned_transfer_matrices(P, 1, 1)
weight = np.array([0.1, 0.4, 0, 0.2])
Tsim = np.arange(100) * Ts
z = co.tf([1, 0], [1], Ts)
Q = Ts * (0.1 + 0.4 * z ** (-1) + 0 + 0.2 * z ** (-3))
# expected result
H_expected = Pzw[i, j] + Pzu[i, 0] * Q * Pyw[0, j]
_, imp_expected = co.impulse_response(H_expected, Tsim)
imp_expected = imp_expected[0, :]
# actual result
imp_actual = Ss.Qsyn.obtain_time_response_var(weight, (i, j), Tsim, Pzw, Pzu, Pyw)
# # debug plot
# plt.plot(imp_actual)
# plt.plot(imp_expected, '--')
# plt.show()
np.testing.assert_allclose(imp_expected, imp_actual, atol=1e-5)