def jsd(freqs1, freqs2, validate=False):
"""
Parameters
----------
freqs1 : one dimensional array
row vector frequencies, sum to 1
freqs2 : one dimensional array
row vector frequencies, sum to 1
validate : bool
Returns
-------
the mathematical calculation of Jensen–Shannon divergence
between two probability distributions
"""
# Convert input arrays into numpy arrays
freqs1 = array(freqs1)
freqs2 = array(freqs2)
if validate:
assert_equal(freqs1.shape,
freqs2.shape,
err_msg="freqs1/freqs2 mismatched shape")
assert freqs1.ndim == 1, "freqs1 has incorrect dimension"
assert freqs2.ndim == 1, "freqs2 has incorrect dimension"
assert_allclose(sum(freqs1), 1, err_msg="invalid freqs1")
assert_allclose(sum(freqs2), 1, err_msg="invalid freqs2")
H_mn = safe_p_log_p(freqs1 / 2 + freqs2 / 2).sum()
mn_H = sum([sum(i) for i in map(safe_p_log_p, [freqs1, freqs2])]) / 2
return H_mn - mn_H
def jsd(freqs1, freqs2, validate=False):
"""calculate Jensen–Shannon divergence between two probability distributions
Parameters
----------
freqs1 : one dimensional array
row vector frequencies, sum to 1
freqs2 : one dimensional array
row vector frequencies, sum to 1
validate : bool
"""
# Convert input arrays into numpy arrays
freqs1 = array(freqs1)
freqs2 = array(freqs2)
if validate:
assert_equal(freqs1.shape,
freqs2.shape,
err_msg="freqs1/freqs2 mismatched shape")
assert freqs1.ndim == 1, "freqs1 has incorrect dimension"
assert freqs2.ndim == 1, "freqs2 has incorrect dimension"
try:
validate_freqs_array(freqs1)
validate_freqs_array(freqs2)
except ValueError as err:
raise AssertionError("freqs not valid") from err
H_mn = safe_p_log_p(freqs1 / 2 + freqs2 / 2).sum()
mn_H = sum([sum(i) for i in map(safe_p_log_p, [freqs1, freqs2])]) / 2
return H_mn - mn_H
def entropy_terms(self):
"""Returns
-------
entropies : array
Has same dimension as self.array with
safe log operation applied.
"""
entropies = safe_p_log_p(self.array)
return self.template.wrap(entropies)
def test_safe_p_log_p(self):
"""safe_p_log_p: should handle pos/neg/zero/empty arrays"""
# normal valid array
a = array([[4, 0, 8], [2, 16, 4]])
assert_equal(safe_p_log_p(a), array([[-8, 0, -24], [-2, -64, -8]]))
# just zeros
a = array([[0, 0], [0, 0]])
assert_equal(safe_p_log_p(a), array([[0, 0], [0, 0]]))
# negative number -- throw error
with self.assertRaises(FloatingPointError):
safe_p_log_p(array([-4]))
# integer input, float output
assert_allclose(safe_p_log_p(array([3])), array([-4.75488750]))
# empty array
assert_equal(safe_p_log_p(array([])), array([]))
def jsd(freqs1, freqs2, validate=False):
"""calculate Jensen–Shannon divergence between two probability distributions
Parameters
----------
freqs1 : one dimensional array
row vector frequencies, sum to 1
freqs2 : one dimensional array
row vector frequencies, sum to 1
validate : bool
"""
# Convert input arrays into numpy arrays
freqs1 = array(freqs1)
freqs2 = array(freqs2)
if validate:
assert_equal(freqs1.shape,
freqs2.shape,
err_msg="freqs1/freqs2 mismatched shape")
assert freqs1.ndim == 1, "freqs1 has incorrect dimension"
assert freqs2.ndim == 1, "freqs2 has incorrect dimension"
try:
validate_freqs_array(freqs1)
validate_freqs_array(freqs2)
except ValueError as err:
raise AssertionError("freqs not valid") from err
H_mn = fsum(safe_p_log_p(freqs1 / 2 + freqs2 / 2))
mn_H = fsum([fsum(i) for i in map(safe_p_log_p, [freqs1, freqs2])]) / 2
jsd_ = H_mn - mn_H
if jsd_ < 0 and isclose(jsd_, 0, atol=1e-10):
jsd_ = 0
elif jsd_ < 0:
raise ArithmeticError(
f"{jsd_} is negative and below defined precision threshold")
return jsd_
def entropy(self):
"""Shannon entropy per position using log2"""
entropies = safe_p_log_p(self.array)
return entropies.sum(axis=1)
