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_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_mvar_all_missing(ft_ar2_mvar_kw, theta_ar2_mvar,
Yt_ar2_mvar, Xt_ar2_mvar):
"""
Test normal run in multi-variate case missing all measurements
"""
t = 2
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])
Bt = Mt['Bt'][t]
Ft = Mt['Ft'][t]
Qt = Mt['Qt'][t]
expected_xi_t1_0 = Ft.dot(kf.xi_t[t][0]) + Bt.dot(kf.Xt[t])
P_t_0 = kf.P_star_t[t][0]
P_t_t = 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_sequential_update_uni_missing(ft_rw_1, theta_rw, Yt_1d, Xt_1d):
"""
Test run in univariate case with missing y
"""
t = 1
index = 1
ob = index - 1
kf = Filter(ft_rw_1, Yt_1d, Xt_1d, for_smoother=True)
kf.init_attr(theta_rw)
for t_ in range(t + 1):
kf._sequential_update(t_)
K = kf.P_star_t[t][ob] / (kf.P_star_t[t][ob] + kf.Rt[t][ob][ob])
v = kf.Yt[t][ob] - kf.xi_t[t][ob] - kf.Dt[t][ob].dot(kf.Xt[t])
expected_xi_t_11 = np.array([[np.nan]])
expected_P_t_11 = np.zeros((1, 1)) * np.nan
expected_P_t1_0 = kf.Ft[t].dot(kf.P_star_t[t][0]).dot(kf.Ft[t]) + kf.Qt[t]
expected_xi_t1_0 = kf.Ft[t].dot(kf.xi_t[t][0]) + \
kf.Bt[t].dot(kf.Xt[t])
np.testing.assert_array_equal(expected_xi_t_11, kf.xi_t[t][1])
np.testing.assert_array_equal(expected_P_t_11, kf.P_star_t[t][1])
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_sequential_update_uni(ft_rw_1, theta_rw, Yt_1d, Xt_1d):
"""
Test normal run in univariate case
"""
t = 0
index = 1
ob = index - 1
kf = Filter(ft_rw_1, Yt_1d, Xt_1d, for_smoother=True)
kf.init_attr(theta_rw)
kf._sequential_update(t)
K = kf.P_star_t[t][ob] / (kf.P_star_t[t][ob] + kf.Rt[t][ob][ob])
v = kf.Yt[t][ob] - kf.xi_t[t][ob] - kf.Dt[t][ob].dot(kf.Xt[t])
expected_xi_t_11 = kf.xi_t[t][ob] + K * v
expected_P_t_11 = kf.P_star_t[t][ob].dot(
kf.Rt[t][ob][ob]) / (kf.P_star_t[t][ob] + kf.Rt[t][ob][ob])
expected_P_t1_0 = kf.Ft[t].dot(expected_P_t_11).dot(kf.Ft[t]) + kf.Qt[t]
expected_xi_t1_0 = kf.Ft[t].dot(expected_xi_t_11) + \
kf.Bt[t].dot(kf.Xt[t])
np.testing.assert_array_almost_equal(expected_xi_t_11, kf.xi_t[t][1])
np.testing.assert_array_almost_equal(expected_P_t_11, kf.P_star_t[t][1])
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])
