def test_categorical():
p = np.array([0.25, 0.5, 0.25])
cat = util.Categorical(p)
X = cat.sample(1000000)
f = np.bincount(X).astype(float)
f /= f.sum()
assert util.eq_delta(f, p, 1e-2)
def test_hmm_1():
pE = np.array([
[0.4, 0.2, 0.4],
[0.0, 0.9, 0.1],
[0.1, 0.1, 0.8]
])
pT = np.array([
[0.5 , 0.5, 0.0 ],
[0.0 , 0.25, 0.75],
[0.75, 0.25, 0.0 ]
])
H = hmm.FixedHMM(
pZ = np.repeat(1.0/3.0, 3),
pE = pE,
pT = pT
)
pS = pE.T.dot(
np.linalg.matrix_power(pT, 1000)[0,:])
n = 100000
X, Z = H.generate(n)
f = np.bincount(X).astype(float)
f /= f.sum()
assert util.eq_delta(pS, f, 1e-2)
fb = H.forward_backward(X)
xi1 = np.zeros(pT.shape)
for i in xrange(n - 1):
xi1[Z[i], Z[i+1]] += 1.0
xi1 /= xi1.sum()
xi2 = fb.xi
xi2 /= xi2.sum()
assert util.eq_delta(xi1, xi2, 1e-2)
gamma1 = np.zeros(pT.shape[0])
for i in xrange(n):
gamma1[Z[i]] += 1.0
gamma1 /= gamma1.sum()
gamma2 = fb.gamma.sum(axis=1)
gamma2 /= gamma2.sum()
assert util.eq_delta(gamma1, gamma2, 1e-2)
