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_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])
