def testNumericalPartitionIsAccurate(self):
"""Test _numerical_base_partition_function against some golden data."""
for (numer, denom) in [(0, 1), (1, 8), (1, 2), (1, 1), (2, 1), (8, 1)]:
alpha = tf.cast(numer, tf.float64) / tf.cast(denom, tf.float64)
z_true = distribution.analytical_base_partition_function(
numer, denom)
z = fit_partition_spline.numerical_base_partition_function(alpha)
self.assertAllClose(z, z_true, atol=1e-10, rtol=1e-10)
def testLogPartitionFractionsAreAccurate(self, float_dtype):
"""Test that the partition function is correct for [0/11, ... 22/11]."""
numers = range(0, 23)
denom = 11
log_zs_true = [
np.log(distribution.analytical_base_partition_function(n, denom))
for n in numers
]
log_zs = self._distribution.log_base_partition_function(
float_dtype(np.array(numers)) / float_dtype(denom))
self.assertAllClose(log_zs, log_zs_true, atol=1e-7, rtol=1e-7)
def _log_partition_fractions_are_accurate(self, float_dtype):
"""Test that the partition function is correct for [0/11, ... 22/11]."""
numers = range(0, 23)
denom = 11
log_zs_true = [
np.log(distribution.analytical_base_partition_function(n, denom))
for n in numers
]
with self.session():
log_zs = distribution.log_base_partition_function(
float_dtype(np.array(numers)) / float_dtype(denom)).eval()
self.assertAllClose(log_zs, log_zs_true, atol=1e-7, rtol=1e-7)
def testAnalyaticalPartitionIsCorrect(self):
"""Tests _analytical_base_partition_function against some golden data."""
# Here we enumerate a set of positive rational numbers n/d alongside
# numerically approximated values of Z(n / d) up to 10 digits of precision,
# stored as (n, d, Z(n/d)). This was generated with an external mathematica
# script.
ground_truth_rational_partitions = (
(1, 7, 4.080330073), (1, 6, 4.038544331), (1, 5, 3.984791180),
(1, 4, 3.912448576), (1, 3, 3.808203509), (2, 5, 3.735479786),
(3, 7, 3.706553276), (1, 2, 3.638993131), (3, 5, 3.553489270),
(2, 3, 3.501024540), (3, 4, 3.439385624), (4, 5, 3.404121259),
(1, 1, 3.272306973), (6, 5, 3.149249092), (5, 4, 3.119044506),
(4, 3, 3.068687433), (7, 5, 3.028084866), (3, 2, 2.965924889),
(8, 5, 2.901059987), (5, 3, 2.855391798), (7, 4, 2.794052016),
(7, 3, 2.260434598), (5, 2, 2.218882601), (8, 3, 2.190349858),
(3, 1, 2.153202857), (4, 1, 2.101960916), (7, 2, 2.121140098),
(5, 1, 2.080000512), (9, 2, 2.089161164), (6, 1, 2.067751267),
(7, 1, 2.059929623), (8, 1, 2.054500222), (10, 3, 2.129863884),
(11, 3, 2.113763384), (13, 3, 2.092928254), (14, 3, 2.085788350),
(16, 3, 2.075212740), (11, 2, 2.073116001), (17, 3, 2.071185791),
(13, 2, 2.063452243), (15, 2, 2.056990258)) # pyformat: disable
for numer, denom, z_true in ground_truth_rational_partitions:
z = distribution.analytical_base_partition_function(numer, denom)
self.assertAllClose(z, z_true, atol=1e-9, rtol=1e-9)
