def test_kl_zero(self):
nchannels = 3
distr = np.array([0.1, 0.3, 0.05, 0.05, 0.2, 0.1, 0.1, 0.1])
# same states, KL divergence should converge to zero
states = np.random.multinomial(1, distr, size=100000).argmax(1)
states2 = np.random.permutation(states)
distr = kl_tools.states2distr(states, nchannels)
distr2 = kl_tools.states2distr(states2, nchannels)
kl1 = kl_tools.mean_KL_estimate(distr, distr2)
assert_almost_equal(kl1, 0., 3)
distr = kl_tools.states2dict(states[:,None], nchannels)
distr2 = kl_tools.states2dict(states2[:,None], nchannels)
kl2, _ = kl_tools.kl_estimation(distr, distr2, 100000)
assert_almost_equal(kl2, 0., 3)
def test_entropy(self):
nchannels = 4
# uniform distribution, entropy = number of channels
alpha = np.zeros(2**nchannels) + 10000
hest = -kl_tools.mean_H_estimate(alpha)
assert(abs(hest-nchannels) < 1e-4)
# sample from distribution, reconstruct entropy
nchannels = 3
distr = np.array([0.1, 0.3, 0.05, 0.05, 0.2, 0.1, 0.1, 0.1])
real_entropy = -sum(distr*np.log2(distr))
h = - kl_tools.entropy(distr)
assert_almost_equal(real_entropy, h, 2)
hest1 = - kl_tools.mean_H_estimate(distr*100000)
assert_almost_equal(real_entropy, hest1, 2)
# sample from distribution
states = np.random.multinomial(1, distr, size=100000).argmax(1)
distr = kl_tools.states2dict(states[:,None], nchannels)
hest1 = - kl_tools.mean_H_estimate(distr[1][0])
assert_almost_equal(real_entropy, hest1, 2)
hest2 = - kl_tools.h_estimation(distr, states.shape[0]);
assert_almost_equal(real_entropy, hest2, 2)
def test_kl(self):
nchannels = 3
distr = np.array([0.1, 0.3, 0.05, 0.05, 0.2, 0.1, 0.1, 0.1])
distr2 = np.array([0.4, 0.2, 0.01, 0.09, 0.05, 0.05, 0.03, 0.17])
real_kl = (distr * np.log2(distr/distr2)).sum()
kl1 = kl_tools.kl(distr, distr2)
assert_almost_equal(kl1, real_kl, 6)
kl2 = kl_tools.mean_KL_estimate(distr*100000, distr2*100000)
assert_almost_equal(kl2, real_kl, 3)
# sample states
states = np.random.multinomial(1, distr, size=100000).argmax(1)
states2 = np.random.multinomial(1, distr2, size=100000).argmax(1)
distr = kl_tools.states2dict(states[:,None], nchannels)
distr2 = kl_tools.states2dict(states2[:,None], nchannels)
kl3, _ = kl_tools.kl_estimation(distr, distr2, 100000)
assert_almost_equal(kl3, real_kl, 2)
def test_states2dict(self):
states = np.array([0]*10 + [1]*10 + [2]*10 + [3]*10)
distr = kl_tools.states2dict(states, 2, states.shape[0], shuffle=False)
assert_array_equal(distr[1][0], [10.,10.,10.,10.])
assert_array_equal(distr[2][0], [10.,10.,0.,0.])
assert_array_equal(distr[2][1], [0.,0.,10.,10.])
for i in range(4):
desired = np.zeros((4,))
desired[i] = 10.
assert_array_equal(distr[4][i], desired)
# check that shuffling shuffles
distr = kl_tools.states2dict(states, 2, states.shape[0], shuffle=True)
assert_array_equal(distr[1][0], [10.,10.,10.,10.])
self.assertFalse(np.all(distr[2][0] == [10.,10.,0.,0.]))
self.assertEqual(distr[2][0].sum(), 20.)
self.assertFalse(np.all(distr[2][1] == [0.,0.,10.,10.]))
self.assertEqual(distr[2][1].sum(), 20.)
for i in range(4):
desired = np.zeros((4,))
desired[i] = 10.
self.assertFalse(np.all(distr[4][i] == desired))
self.assertEqual(distr[4][i].sum(), 10.)