def test_LDL_first_missing(ft_mvar, theta_mvar_diffuse, Yt_mvar, Xt_mvar):
"""
Test when first measurement is missing
"""
kf = Filter(ft_mvar, Yt_mvar, Xt_mvar, for_smoother=True)
kf.init_attr(theta_mvar_diffuse)
Y_t, H_t, D_t, R_t, L_t, L_inv = kf._LDL(1)
assert kf.n_t[1] == 2
R_t_move = np.array([[4, 3, 2], [3, 6, 1], [2, 1, 3]])
L_t_expected, R_t_expected, _ = linalg.ldl(R_t_move)
L_inv_expected, _ = linalg.lapack.dtrtri(L_t_expected, lower=True)
np.testing.assert_array_equal(L_t, L_t_expected)
np.testing.assert_array_equal(R_t, R_t_expected)
Y_t_expected = linalg.pinv(L_t_expected).dot(
np.array([2.2, 3, 0]).reshape(-1, 1))
np.testing.assert_array_almost_equal(Y_t, Y_t_expected)
H_t_expected = L_inv_expected.dot(np.array([2, 2.4, 1]).reshape(-1, 1))
np.testing.assert_array_almost_equal(H_t, H_t_expected)
expected_partitioned_index = np.array([1, 2, 0])
np.testing.assert_array_equal(kf.partitioned_index[1],
expected_partitioned_index)
def test_LDL(ft_mvar, theta_mvar_diffuse, Yt_mvar, Xt_mvar):
"""
Test normal run
"""
kf = Filter(ft_mvar, Yt_mvar, Xt_mvar, for_smoother=True)
kf.init_attr(theta_mvar_diffuse)
Y_t, H_t, D_t, R_t, L_t, L_inv = kf._LDL(0)
assert kf.n_t[0] == 3
R_t_move = np.array([[3, 2, 1], [2, 4, 3], [1, 3, 6]])
L_t_expected, R_t_expected, _ = linalg.ldl(R_t_move)
L_inv_expected, _ = linalg.lapack.dtrtri(L_t_expected, lower=True)
np.testing.assert_array_equal(L_t, L_t_expected)
np.testing.assert_array_equal(R_t, R_t_expected)
Y_t_expected = linalg.pinv(L_t_expected).dot(
np.array([1, 2, 2.1]).reshape(-1, 1))
np.testing.assert_array_almost_equal(Y_t, Y_t_expected)
H_t_expected = L_inv_expected.dot(np.array([1, 2, 2.4]).reshape(-1, 1))
np.testing.assert_array_almost_equal(H_t, H_t_expected)
expected_partitioned_index = np.array([0, 1, 2])
np.testing.assert_array_equal(kf.partitioned_index[0],
expected_partitioned_index)
def test_G_explosive_root(f_arma32):
"""
Test how to handle explosive root in Smoother
"""
# Initialize the model
x = 1 # used to calculate stationary mean
model = BCM()
model.set_f(f_arma32)
theta_intend = np.array([0.1, 0.2, 0.25])
theta_test = np.array([0.59358299, 0.91708496, 0.54634604])
T = 250
my_ft = lambda theta, T, **kwargs: ft(theta, f_arma32, T, **kwargs)
x_col = ['const']
Xt = pd.DataFrame({x_col[0]: x * np.ones(T)})
# Build simulated data
df, y_col, xi_col = model.simulated_data(input_theta=theta_intend, Xt=Xt)
Xt = df_to_tensor(df, x_col)
Yt = df_to_tensor(df, y_col)
kf = Filter(my_ft, Yt, Xt, for_smoother=True)
kf.fit(theta_test)
ks = Smoother()
ks.fit(kf)
result = ks.G(theta_test)
assert not np.isnan(result)
def test_E_chi2(ft_ll_mvar_diffuse, theta_ll_mvar_diffuse,
Yt_mvar_diffuse_smooth):
"""
Test normal run
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_smooth, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
ks = Smoother()
ks.fit(kf)
theta_test = theta_ll_mvar_diffuse + 1
Mt = ft_ll_mvar_diffuse(theta_test, ks.T)
# Test first missing
t = 2
chi2 = ks._E_chi2(Mt, t)
Ht = Mt['Ht'][t][1]
Dt = Mt['Dt'][t][1]
e_chi = ks.Yt[t][0] - Ht.dot(ks.xi_t_T[t]) - \
Dt.dot(ks.Xt[t])
e_chi2 = e_chi.dot(e_chi.T) + Ht.dot(ks.P_t_T[t]).dot(Ht.T)
np.testing.assert_array_equal(e_chi2, chi2)
# # Test all present
t = 3
chi2 = ks._E_chi2(Mt, t)
Ht = Mt['Ht'][t]
Dt = Mt['Dt'][t]
e_chi = ks.Yt[t] - Ht.dot(ks.xi_t_T[t]) - \
Dt.dot(ks.Xt[t])
e_chi2 = e_chi.dot(e_chi.T) + Ht.dot(ks.P_t_T[t]).dot(Ht.T)
np.testing.assert_array_equal(e_chi2, chi2)
def test_init_attr_diffuse(ft_mvar, theta_mvar_diffuse, Yt_mvar, Xt_mvar):
"""
Test if init_attr for diffuse
"""
kf = Filter(ft_mvar, Yt_mvar, Xt_mvar, for_smoother=True)
kf.init_attr(theta_mvar_diffuse)
assert kf.q == 1 and \
len(kf.L0_t[0]) == Yt_mvar[0].shape[0]
def test_init_attr_input(ft_mvar, theta_mvar, Yt_mvar, Xt_mvar):
"""
Test normal run
"""
kf = Filter(ft_mvar, Yt_mvar, Xt_mvar, for_smoother=True)
kf.init_attr(theta_mvar)
assert len(kf.L_star_t) == len(Yt_mvar) and \
len(kf.L_star_t[0]) == Yt_mvar[0].shape[0]
def test_get_filtered_val_missing(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
"""
Test missing measurements handling
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
Yt_filtered, Yt_filtered_cov, _, _ = kf.get_filtered_val()
np.testing.assert_array_equal(kf.Ht[2].dot(kf.xi_t[2][0]), Yt_filtered[2])
def test_get_filtered_val_not_filtered(ft_ll_mvar_1d, Yt_mvar_diffuse_missing):
"""
Test error message when fit is not run
"""
kf = Filter(ft_ll_mvar_1d, Yt_mvar_diffuse_missing, for_smoother=True)
with pytest.raises(TypeError) as error:
kf.get_filtered_val()
expected_result = 'The Kalman filter object is not fitted yet'
result = str(error.value)
assert result == expected_result
def test_get_filtered_state_not_fitted(ft_ll_mvar_diffuse,
Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
t = 6
with pytest.raises(ValueError) as error:
result = kf.get_filtered_state(t)
expected_result = 'Kalman filter is not fitted yet'
result = str(error.value)
assert expected_result == result
def test_get_filtered_y_no_xi(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
"""
Test df without xi
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
Yt_filtered, Yt_filtered_cov, xi_t, P_t = kf.get_filtered_val(is_xi=False)
assert np.isnan(xi_t[-1])
assert np.isnan(P_t[-1])
def test_get_filtered_state_max(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
t = 6
with pytest.raises(ValueError) as error:
result = kf.get_filtered_state(t)
expected_result = 'Maximum t allowed is 4'
result = str(error.value)
assert expected_result == result
def test_get_filtered_val_all_xi(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
"""
Test df with all xi
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
Yt_filtered, Yt_filtered_cov, xi_t, P_t = kf.get_filtered_val()
np.testing.assert_array_equal(xi_t[2], kf.xi_t[2][0])
np.testing.assert_array_equal(P_t[2], np.nan * np.ones(P_t[2].shape))
np.testing.assert_array_equal(P_t[3], kf.P_star_t[3][0])
def test_get_filtered_state_diffuse(ft_ll_mvar_diffuse,
Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
t = 1
with pytest.raises(ValueError) as error:
result = kf.get_filtered_state(t)
expected_result = 'Diffuse state at time 1'
result = str(error.value)
assert expected_result == result
def test_get_smoothed_val_all_xi(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
"""
Test df with all xi
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
ks = Smoother()
ks.fit(kf)
y_t_T, yP_t_T, xi_T, P_T = ks.get_smoothed_val()
np.testing.assert_array_equal(xi_T[2], ks.xi_t_T[2])
np.testing.assert_array_equal(P_T[2], ks.P_t_T[2])
np.testing.assert_array_equal(P_T[3], ks.P_t_T[3])
Mt = ft_ll_mvar_diffuse(theta_ll_mvar_diffuse, 4)
Rt = Mt['Rt'][0]
Dt = Mt['Dt'][0]
Ht = Mt['Ht'][0]
# Test smoothed y
R2_0 = np.array([[0.5 - 0.4 / 0.6 * 0.4]])
B0 = 0.4 / 0.6
delta_H0 = Ht[0:1] - B0 * Ht[1:]
eps0 = B0 * (Yt_mvar_diffuse_missing[0][1] - Dt[1:].dot(ks.Xt[0]) -
Ht[1:].dot(ks.xi_t_T[0]))
y0 = Ht[0:1].dot(ks.xi_t_T[0]) + Dt[0:1].dot(ks.Xt[0]) + eps0
yP_0 = (delta_H0.dot(ks.P_t_T[0]).dot(delta_H0.T) + R2_0).item()
R2_2 = np.array([[0.6 - 0.4 / 0.5 * 0.4]])
B2 = 0.4 / 0.5
delta_H2 = Ht[1] - B2 * Ht[0]
eps2 = B2 * (Yt_mvar_diffuse_missing[2][0] - Dt[:1].dot(ks.Xt[2]) -
Ht[:1].dot(ks.xi_t_T[2]))
y2 = Ht[1:].dot(ks.xi_t_T[2]) + Dt[1:].dot(ks.Xt[2]) + eps2
yP_2 = (delta_H2.dot(ks.P_t_T[2]).dot(delta_H2.T) + R2_2).item()
expected_y_t_T = [
np.array([[y0], [2]]),
Ht.dot(ks.xi_t_T[1] + Dt.dot(ks.Xt[1])),
np.array([[2.5], [y2]]),
np.array([[3], [5]])
]
expected_Pcov_T = [
np.array([[yP_0, 0], [0, 0]]),
ks.Ht[1].dot(ks.P_t_T[1]).dot(ks.Ht[1].T) + ks.Rt[1],
np.array([[0, 0], [0, yP_2]]),
np.zeros([2, 2])
]
for t in range(4):
np.testing.assert_array_almost_equal(yP_t_T[t], expected_Pcov_T[t])
np.testing.assert_array_almost_equal(y_t_T[t], expected_y_t_T[t])
def test_joseph_form(ft_ar1, theta_ar1, Yt_1d):
"""
Test normal run
"""
kf = Filter(ft_ar1, Yt_1d, for_smoother=True)
L = np.array([[2, 3], [4, 5]])
P = np.array([[3, 4], [4, 5]])
KRK = np.ones([2, 2])
result = kf._joseph_form(L, P, KRK=KRK)
expected_result = np.array([[106, 188], [188, 334]])
np.testing.assert_array_equal(result, expected_result)
def test_init_attr_smoother_not_for_smoother(ft_rw_1, theta_rw, Yt_1d, Xt_1d):
"""
Test error message Kalman filter not for smoother
"""
kf = Filter(ft_rw_1, Yt_1d, Xt_1d, for_smoother=False)
kf.fit(theta_rw)
ks = Smoother()
with pytest.raises(TypeError) as error:
ks.init_attr_smoother(kf)
msg = str(error.value)
e_msg = 'The Kalman filter object is not for smoothers'
assert msg == e_msg
def test_init_attr_smoother_diffuse(ft_ll_mvar_diffuse, theta_ll_mvar_diffuse,
Yt_mvar_diffuse_missing):
"""
Test initialization for diffuse smoother
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
ks = Smoother()
ks.init_attr_smoother(kf)
e_r1 = np.zeros([2, 1])
e_N1 = np.zeros([2, 2])
np.testing.assert_array_equal(e_r1, ks.r1_t[ks.t_q - 1])
np.testing.assert_array_equal(e_N1, ks.N1_t[ks.t_q - 1])
assert ks.t_q == 3
def test_get_smoothed_y_selected_xi(ft_ll_mvar_diffuse,
Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
"""
Test df with selected xi
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
ks = Smoother()
ks.fit(kf)
_, _, xi_T, P_T = ks.get_smoothed_val(xi_col=[1])
np.testing.assert_array_equal(xi_T[2], ks.xi_t_T[2][[1]])
np.testing.assert_array_equal(P_T[2], ks.P_t_T[2][[1]][:, [1]])
def test_over_ride_error_input(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
"""
Raises exception when init_state wrong input
"""
init_val = {
'P_star_t': np.zeros([2]),
'xi_t': 100 * np.ones([2, 1]),
'q': 0
}
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
with pytest.raises(ValueError) as error:
kf.fit(theta_ll_mvar_diffuse, init_state=init_val)
expected_result = 'User-specified P_star_t does not have 2 dimensions'
result = str(error.value)
assert expected_result == result
def test_get_filtered_state_T(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
t = kf.T
result = kf.get_filtered_state(t)
expected_result = {
'P_star_t': kf.P_T1,
'P_inf_t': np.zeros([2, 2]),
'xi_t': kf.xi_T1,
'q': 0
}
for i in ['P_star_t', 'P_inf_t', 'xi_t']:
np.testing.assert_array_equal(result[i], expected_result[i])
assert result['q'] == expected_result['q']
def test_init_attr_smoother(ft_rw_1, theta_rw, Yt_1d, Xt_1d):
"""
Test normal run
"""
kf = Filter(ft_rw_1, Yt_1d, Xt_1d, for_smoother=True)
kf.fit(theta_rw)
ks = Smoother()
ks.init_attr_smoother(kf)
e_r0 = np.zeros([1, 1])
e_N0 = np.zeros([1, 1])
r0 = ks.r0_t[kf.T - 1]
N0 = ks.N0_t[kf.T - 1]
np.testing.assert_array_equal(e_r0, r0)
np.testing.assert_array_equal(e_N0, N0)
assert ks.r1_t.shape[0] == 0
def test_sequential_update_mvar_missing_first(ft_ar2_mvar_kw, theta_ar2_mvar,
Yt_ar2_mvar, Xt_ar2_mvar):
"""
Test normal run in multi-variate case missing middle measurements
"""
t = 3
kf = Filter(ft_ar2_mvar_kw, Yt_ar2_mvar, Xt_ar2_mvar, for_smoother=True)
kf.init_attr(theta_ar2_mvar)
for t_ in range(t + 1):
kf._sequential_update(t_)
Mt = kf.ft(kf.theta, kf.T, x_0=Xt_ar2_mvar[0])
Ht = Mt['Ht'][t][[1, 2]]
Bt = Mt['Bt'][t]
Dt = Mt['Dt'][t][[1, 2]]
Ft = Mt['Ft'][t]
Qt = Mt['Qt'][t]
Rt = Mt['Rt'][t][[1, 2]][:, [1, 2]]
Upsilon = Ht.dot(kf.P_star_t[t][0]).dot(Ht.T) + Rt
K = kf.P_star_t[t][0].dot(Ht.T).dot(linalg.pinvh(Upsilon))
v = kf.Yt[t][[0, 1]] - Ht.dot(kf.xi_t[t][0]) - Dt.dot(kf.Xt[t])
expected_xi_t_nt = kf.xi_t[t][0] + K.dot(v)
P_t_0 = kf.P_star_t[t][0]
P_t_t = P_t_0 - P_t_0.dot(Ht.T).dot(
linalg.pinvh(Upsilon)).dot(Ht).dot(P_t_0)
expected_P_t_nt = P_t_t
np.testing.assert_array_almost_equal(expected_P_t_nt,
kf.P_star_t[t][kf.n_t[t]])
np.testing.assert_array_almost_equal(expected_xi_t_nt,
kf.xi_t[t][kf.n_t[t]])
def test_sequential_update_mvar_full_obs(ft_ar2_mvar_kw, theta_ar2_mvar,
Yt_ar2_mvar, Xt_ar2_mvar):
"""
Test normal run in multi-variate case full measurements
"""
t = 0
kf = Filter(ft_ar2_mvar_kw, Yt_ar2_mvar, Xt_ar2_mvar, for_smoother=True)
kf.init_attr(theta_ar2_mvar)
kf._sequential_update(t)
Mt = kf.ft(kf.theta, kf.T, x_0=Xt_ar2_mvar[0])
Ht = Mt['Ht'][t]
Bt = Mt['Bt'][t]
Dt = Mt['Dt'][t]
Ft = Mt['Ft'][t]
Qt = Mt['Qt'][t]
Rt = Mt['Rt'][t]
Upsilon = Ht.dot(kf.P_star_t[t][0]).dot(Ht.T) + Rt
K = kf.P_star_t[t][0].dot(Mt['Ht'][t].T).dot(linalg.pinvh(Upsilon))
v = kf.Yt[t] - Ht.dot(kf.xi_t[t][0]) - Dt.dot(kf.Xt[t])
expected_xi_t1_0 = Ft.dot(kf.xi_t[t][0] + K.dot(v)) + Bt.dot(kf.Xt[t])
P_t_0 = kf.P_star_t[t][0]
P_t_t = P_t_0 - P_t_0.dot(Ht.T).dot(
linalg.pinvh(Upsilon)).dot(Ht).dot(P_t_0)
expected_P_t1_0 = Ft.dot(P_t_t).dot(Ft.T) + Qt
np.testing.assert_array_almost_equal(expected_P_t1_0,
kf.P_star_t[t + 1][0])
np.testing.assert_array_almost_equal(expected_xi_t1_0, kf.xi_t[t + 1][0])
def test_get_filtered_state_t(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
"""
get values at t < self.T
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
t = kf.T - 1
result = kf.get_filtered_state(t)
expected_result = {
'P_star_t': kf.P_star_t[t][0],
'P_inf_t': kf.P_inf_t[t][0],
'xi_t': kf.xi_t[t][0],
'q': 0
}
for i in ['P_star_t', 'P_inf_t', 'xi_t']:
np.testing.assert_array_equal(result[i], expected_result[i])
assert result['q'] == expected_result['q']
def test_get_smoothed_val_not_smoothed(ft_ll_mvar_1d, Yt_1d):
"""
Test error message when fit is not run
"""
kf = Filter(ft_ll_mvar_1d, Yt_1d, for_smoother=True)
ks = Smoother()
with pytest.raises(TypeError) as error:
ks.get_smoothed_val()
expected_result = 'The Kalman smoother object is not fitted yet'
result = str(error.value)
assert result == expected_result
def test_E_delta2(ft_ll_mvar_diffuse, theta_ll_mvar_diffuse,
Yt_mvar_diffuse_smooth):
"""
Test normal run
"""
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_smooth, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse)
ks = Smoother()
ks.fit(kf)
t = 2
theta_test = [i + 0.1 for i in theta_ll_mvar_diffuse]
Mt = ft_ll_mvar_diffuse(theta_test, ks.T)
delta2 = ks._E_delta2(Mt, t)
nt = ks.xi_t_T[t] - Mt['Ft'][t-1].dot(ks.xi_t_T[t-1]) - \
Mt['Bt'][t-1].dot(ks.Xt[t-1])
e_delta2 = nt.dot(nt.T) + ks.P_t_T[t] + Mt['Ft'][t - 1].dot(
ks.P_t_T[t - 1]).dot(Mt['Ft'][t - 1].T) - Mt['Ft'][t - 1].dot(
ks.Pcov_t_t1[t - 1]) - (ks.Pcov_t_t1[t - 1].T).dot(
Mt['Ft'][t - 1].T)
np.testing.assert_array_almost_equal(e_delta2, delta2)
def test_over_ride(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing,
theta_ll_mvar_diffuse):
"""
Force a diffuse kalman filter to become regular filter
"""
init_val = {
'P_star_t': np.zeros([2, 2]),
'xi_t': 100 * np.ones([2, 1]),
'q': 0
}
kf = Filter(ft_ll_mvar_diffuse, Yt_mvar_diffuse_missing, for_smoother=True)
kf.fit(theta_ll_mvar_diffuse, init_state=init_val)
t = 0
result = kf.get_filtered_state(t)
expected_result = {
'P_star_t': np.zeros([2, 2]),
'P_inf_t': np.zeros([2, 2]),
'xi_t': 100 * np.ones([2, 1]),
'q': 0
}
for i in ['P_star_t', 'P_inf_t', 'xi_t']:
np.testing.assert_array_equal(result[i], expected_result[i])
assert result['q'] == expected_result['q']
def test_sequential_update_diffuse_ll_1d(ft_ll_1d_diffuse, theta_ll_1d_diffuse,
Yt_1d_full):
"""
Test local linear models from chapter 5 of Koopman and Durbin (2012)
"""
t = 3
kf = Filter(ft_ll_1d_diffuse, Yt_1d_full, for_smoother=True)
kf.init_attr(theta_ll_1d_diffuse)
for t_ in range(t):
kf._sequential_update_diffuse(t_)
# Test period 0 result
q1 = theta_ll_1d_diffuse[0] / theta_ll_1d_diffuse[2]
q2 = theta_ll_1d_diffuse[1] / theta_ll_1d_diffuse[2]
e_P_inf_t1_0 = np.ones([2, 2])
e_P_star_t1_0 = np.array([[1 + q1, 0], [0, q2]]) * theta_ll_1d_diffuse[2]
e_xi_t1_0 = np.array([[Yt_1d_full[0][0]], [0]])
np.testing.assert_array_almost_equal(e_P_inf_t1_0, kf.P_inf_t[1][0])
np.testing.assert_array_almost_equal(e_xi_t1_0, kf.xi_t[1][0])
np.testing.assert_array_almost_equal(e_P_star_t1_0, kf.P_star_t[1][0])
# Test period 1 result
e_P_inf_t1_0 = np.zeros([2, 2])
e_P_star_t1_0 = np.array([[5 + 2 * q1 + q2, 3 + q1 + q2],
[3 + q1 + q2, 2 + q1 + 2 * q2]]) * \
theta_ll_1d_diffuse[2]
y2 = Yt_1d_full[1][0][0]
y1 = Yt_1d_full[0][0][0]
e_xi_t1_0 = np.array([[2 * y2 - y1], [y2 - y1]])
np.testing.assert_array_almost_equal(e_P_inf_t1_0, kf.P_inf_t[2][0])
np.testing.assert_array_almost_equal(e_xi_t1_0, kf.xi_t[2][0])
np.testing.assert_array_almost_equal(e_P_star_t1_0, kf.P_star_t[2][0])
# Test period 2 result, should return same result as _sequential_update()
P_inf_t1_0 = kf.P_inf_t[3][0].copy()
P_star_t1_0 = kf.P_star_t[3][0].copy()
xi_t1_0 = kf.xi_t[3][0].copy()
kf._sequential_update(2)
np.testing.assert_array_almost_equal(P_inf_t1_0, np.zeros([2, 2]))
np.testing.assert_array_almost_equal(xi_t1_0, kf.xi_t[3][0])
np.testing.assert_array_almost_equal(P_star_t1_0, kf.P_star_t[3][0])
def test_sequential_update_diffuse_update_multiple_q(ft_q,
theta_ll_mvar_diffuse,
Yt_q):
"""
For ll model, only measurements across time can reduce rank of P_inf_t
"""
t = 1
kf = Filter(ft_q, Yt_q, for_smoother=True)
kf.init_attr(theta_ll_mvar_diffuse)
kf._sequential_update_diffuse(0)
assert kf.q == 0
def test_sequential_update_diffuse_missing(ft_rw_1_diffuse, theta_rw,
Yt_1d_missing, Xt_1d):
"""
Test first missing
"""
t = 0
kf = Filter(ft_rw_1_diffuse, Yt_1d_missing, Xt_1d, for_smoother=True)
kf.init_attr(theta_rw)
for t_ in range(t + 1):
kf._sequential_update_diffuse(t_)
e_P_inf_t1_0 = np.array([[1]])
e_xi_t1_0 = np.array([[0]])
np.testing.assert_array_almost_equal(e_P_inf_t1_0, kf.P_inf_t[t + 1][0])
np.testing.assert_array_almost_equal(e_xi_t1_0, kf.xi_t[t + 1][0])