def _estimate(T):
"""Estimate PID for a given target."""
# Goettingen estimator
pid_goettingen = SxPID(SETTINGS)
tic = tm.time()
est_goettingen = pid_goettingen.estimate([X, Y], T)
t_goettingen = tm.time() - tic
print('\nCopied source')
print('Estimator SxPID\n')
print('PID evaluation {:.3f} s\n'.format(t_goettingen))
print('Uni s1 {0:.8f}'.format(
est_goettingen['avg'][((1, ), )][2]))
print('Uni s2 {0:.8f}'.format(
est_goettingen['avg'][((2, ), )][2]))
print('Shared s1_s2 {0:.8f}'.format(est_goettingen['avg'][(
(1, ),
(2, ),
)][2]))
print('Synergy s1_s2 {0:.8f}'.format(est_goettingen['avg'][((
1,
2,
), )][2]))
return est_goettingen
def test_non_binary_alphabet():
"""Test Goettingen estimator on larger alphabets."""
n = 1000
alph_s1 = 5
alph_s2 = 3
s1 = np.random.randint(0, alph_s1, n)
s2 = np.random.randint(0, alph_s2, n)
target = s1 + s2
pid_goettingen = SxPID(SETTINGS)
# Goettingen SxPID estimator
tic = tm.time()
est_goettingen = pid_goettingen.estimate([s1, s2], target)
t_goettingen = tm.time() - tic
print('\nInt addition - N = 1000')
print('Estimator SxPID\n')
print('PID evaluation {:.3f} s\n'.format(t_goettingen))
print('Uni s1 {0:.8f}'.format(
est_goettingen['avg'][((1, ), )][2]))
print('Uni s2 {0:.8f}'.format(
est_goettingen['avg'][((2, ), )][2]))
print('Shared s1_s2 {0:.8f}'.format(est_goettingen['avg'][(
(1, ),
(2, ),
)][2]))
print('Synergy s1_s2 {0:.8f}'.format(est_goettingen['avg'][((
1,
2,
), )][2]))
def test_average_pid_xor_long():
"""Test PID estimation with Goettingen estimator on XOR with higher N."""
# logical XOR - N
n = 1000
alph = 2
s1 = np.random.randint(0, alph, n)
s2 = np.random.randint(0, alph, n)
target = np.logical_xor(s1, s2).astype(int)
print(
'\n\nTesting PID estimator on binary XOR, pointset size: {0}.'.format(
n))
# SxPID estimator
tic = tm.time()
pid_goettingen = SxPID(SETTINGS)
est_goettingen = pid_goettingen.estimate([s1, s2], target)
t_goettingen = tm.time() - tic
print('\nLogical XOR - N = 1000')
print('Estimator SxPID\n')
print('PID evaluation {:.3f} s\n'.format(t_goettingen))
print('Uni s1 {0:.8f}'.format(
est_goettingen['avg'][((1, ), )][2]))
print('Uni s2 {0:.8f}'.format(
est_goettingen['avg'][((2, ), )][2]))
print('Shared s1_s2 {0:.8f}'.format(est_goettingen['avg'][(
(1, ),
(2, ),
)][2]))
print('Synergy s1_s2 {0:.8f}'.format(est_goettingen['avg'][((
1,
2,
), )][2]))
# atol = 10/n since the divergence from the uniform dist of logic xor is in the order of 10/n
assert np.isclose(-0.5849625007211562,
est_goettingen['avg'][(
(1, ),
(2, ),
)][2],
atol=10 / n), ('Average Shared is not -0.5849...')
def test_pointwise_pid_and():
"""Test Goettingen estimator on pointwise level"""
pid_goettingen = SxPID(SETTINGS)
Z = np.logical_and(X, Y).astype(int)
est_goettingen = _estimate(Z)
true_values = {
(0, 0, 0): 0.4150374992788438,
(0, 1, 0): -0.16992500144231237,
(1, 0, 0): -0.16992500144231237,
(1, 1, 1): 0.4150374992788438
}
for i in range(4):
assert np.isclose(
true_values[(X[i], Y[i], Z[i])],
est_goettingen['ptw'][(X[i], Y[i], Z[i])][(
(1, ),
(2, ),
)][2]), ('pointwise shared at ({0},{1},{2}) is not {3:.8f}'.format(
X[i], Y[i], Z[i], est_goettingen['ptw'][(X[i], Y[i], Z[i])][(
(1, ),
(2, ),
)][2]))
def test_average_pid_three_hash():
"""Test Goettingen estimator on binary three hash."""
s1 = np.asarray([0, 0, 0, 0, 1, 1, 1, 1])
s2 = np.asarray([0, 0, 1, 1, 0, 0, 1, 1])
s3 = np.asarray([0, 1, 0, 1, 0, 1, 0, 1])
target = np.logical_xor(s3, np.logical_xor(s1, s2).astype(int)).astype(int)
pid_goettingen = SxPID(SETTINGS)
# Goettingen SxPID estimator
tic = tm.time()
est_goettingen = pid_goettingen.estimate([s1, s2, s3], target)
t_goettingen = tm.time() - tic
print('\n Binary three hash')
print('Estimator SxPID\n')
print(
'PID evaluation (Average) {:.3f} s\n'.
format(t_goettingen))
print('Uni s1 {0:.8f}'.
format(est_goettingen['avg'][((1, ), )][2]))
print('Uni s2 {0:.8f}'.
format(est_goettingen['avg'][((2, ), )][2]))
print('Uni s3 {0:.8f}'.
format(est_goettingen['avg'][((3, ), )][2]))
print('Synergy s1_s2_s3 {0:.8f}'.
format(est_goettingen['avg'][((1, 2, 3), )][2]))
print('Synergy s1_s2 {0:.8f}'.
format(est_goettingen['avg'][((
1,
2,
), )][2]))
print('Synergy s1_s3 {0:.8f}'.
format(est_goettingen['avg'][((
1,
3,
), )][2]))
print('Synergy s2_s3 {0:.8f}'.
format(est_goettingen['avg'][((
2,
3,
), )][2]))
print('Shared s1_s2_s3 {0:.8f}'.
format(est_goettingen['avg'][(
(1, ),
(2, ),
(3, ),
)][2]))
print('Shared of (s1, s2) {0:.8f}'.
format(est_goettingen['avg'][(
(1, ),
(2, ),
)][2]))
print('Shared of (s1, s2) {0:.8f}'.
format(est_goettingen['avg'][(
(1, ),
(3, ),
)][2]))
print('Shared of (s2, s3) {0:.8f}'.
format(est_goettingen['avg'][(
(2, ),
(3, ),
)][2]))
print('Shared of (Synergy s1_s2, Synergy s1_s3) {0:.8f}'.
format(est_goettingen['avg'][(
(
1,
2,
),
(1, 3),
)][2]))
print('Shared of (Synergy s1_s2, Synergy s2_s3) {0:.8f}'.
format(est_goettingen['avg'][(
(
1,
2,
),
(2, 3),
)][2]))
print('Shared of (Synergy s1_s3, Synergy s2_s3) {0:.8f}'.
format(est_goettingen['avg'][(
(
1,
3,
),
(2, 3),
)][2]))
print('Shared of (Synergy s1_s2, Synergy s1_s3, Synergy s2_s3) {0:.8f}'.
format(est_goettingen['avg'][(
(
1,
2,
),
(1, 3),
(2, 3),
)][2]))
print('Shared of (s1, Synergy s2_s3) {0:.8f}'.
format(est_goettingen['avg'][(
(1, ),
(2, 3),
)][2]))
print('Shared of (s2, Synergy s1_s3) {0:.8f}'.
format(est_goettingen['avg'][(
(2, ),
(1, 3),
)][2]))
print('Shared of (s3, Synergy s1_s2) {0:.8f}'.
format(est_goettingen['avg'][(
(3, ),
(1, 2),
)][2]))
assert np.isclose(0.1926450779423959, est_goettingen['avg'][(
(1, ),
(2, ),
(3, ),
)][2]), ('Average Shared is not 0.1926...')
assert np.isclose(-0.22686079328030903, est_goettingen['avg'][(
(
1,
2,
),
(1, 3),
(2, 3),
)][2]), (
'Average Shared of (Synergy s1_s2, Synergy s1_s3, Synergy s2_s3) is not -0.2268...'
)
assert np.isclose(0.24511249783653177, est_goettingen['avg'][((
1, 2, 3), )][2]), ('Average Synergy s1_s2_s3 is not 0.2451...')