def test_gauss_outdistr(self):
p0 = np.array([1, 0])
A = np.array([[0.9, 0.1, 0], [0, 0.9, 0.1]])
mc = MarkovChain(p0, A)
pD_list = []
pD_list.append(GaussDistr(mean=np.array([0]), std=np.array([1])))
pD_list.append(GaussDistr(mean=np.array([3]), std=np.array([2])))
h = HMM(mc, pD_list)
n_states = h.n_states
x = np.array([-0.2, 2.6, 1.3])[:, np.newaxis]
T = x.shape[0]
pX, logS = pD_list[0].prob(x, pD_list)
alpha_hat, c = mc.forward(pX)
beta_hat = mc.backward(pX, c)
logP_hmm = logprob(h, x)
pX_exp = np.array([[1.0000, 0.0695, 1.0000], [0.1418, 1.0000, 0.8111]])
np.testing.assert_array_almost_equal(pX, pX_exp, decimal=4)
alpha_hat_exp = np.array([[1.0000, 0.3847, 0.4189],
[0, 0.6153, 0.5811]])
np.testing.assert_array_almost_equal(alpha_hat,
alpha_hat_exp,
decimal=4)
c_exp = np.array([1.0000, 0.1625, 0.8266, 0.0581])
np.testing.assert_array_almost_equal(c, c_exp, decimal=4)
beta_hat_exp = np.array([[1.0000, 1.0389, 0], [8.4154, 9.3504,
2.0818]])
np.testing.assert_array_almost_equal(beta_hat, beta_hat_exp, decimal=4)
logP_hmm_exp = np.array([-9.1877])
np.testing.assert_array_almost_equal(logP_hmm, logP_hmm_exp, decimal=4)
def test_discrete_outdistr(self):
q1 = np.array([1, 0])
A1 = np.array([[0.9, 0.1, 0], [0, 0.9, 0.1]])
mc = MarkovChain(q1, A1)
pD_list = [
DiscreteDistr(np.array([0.6, 0.3, 0.1])),
DiscreteDistr(np.array([0.1, 0.3, 0.6]))
]
hmm1 = HMM(mc, pD_list)
n_states = hmm1.n_states
Z = np.array([1, 3, 2])
T = len(Z)
pZ, _ = pD_list[0].prob(Z, pD_list)
[alpha_hat, c] = mc.forward(pZ)
expected_alpha_hat = np.array([[1.0000, 0.6000, 0.5625],
[0, 0.4000, 0.4375]])
np.testing.assert_array_almost_equal(alpha_hat,
expected_alpha_hat,
decimal=4)
beta_hat = mc.backward(pZ, c)
expected_beta_hat = np.array([[1.6667, 1.5873, 0],
[12.8571, 14.2857, 7.9365]])
np.testing.assert_array_almost_equal(beta_hat,
expected_beta_hat,
decimal=4)
gamma = np.multiply(np.multiply(alpha_hat, beta_hat),
np.tile(c[0:T], (n_states, 1))) # to check
expected_gamma = np.array([[1.0000, 0.1429, 0], [0, 0.8571, 1.0000]])
np.testing.assert_array_almost_equal(gamma, expected_gamma, decimal=4)
