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# Copyright 2017 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Tests for stateless random-number generation ops."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import math
import numpy as np
from tensorflow.compiler.tests import xla_test
from tensorflow.contrib import stateless
from tensorflow.python.framework import dtypes
from tensorflow.python.ops import array_ops
from tensorflow.python.ops.distributions import special_math
from tensorflow.python.platform import test
class StatelessRandomOpsTest(xla_test.XLATestCase):
"""Test cases for stateless random-number generator operators."""
def _random_types(self):
return self.float_types & {dtypes.float32, dtypes.float64}
def testDeterminism(self):
# Stateless values should be equal iff the seeds are equal (roughly)
with self.cached_session(), self.test_scope():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
seeds = [(x, y) for x in range(5) for y in range(5)] * 3
for stateless_op in [
stateless.stateless_random_uniform, stateless.stateless_random_normal
]:
for shape in (), (3,), (2, 5):
for dtype in self._random_types():
pure = stateless_op(shape, seed=seed_t, dtype=dtype)
values = [(seed, pure.eval(feed_dict={
seed_t: seed
})) for seed in seeds]
for s0, v0 in values:
for s1, v1 in values:
self.assertEqual(s0 == s1, np.all(v0 == v1))
def testRandomUniformIsInRange(self):
with self.cached_session() as sess, self.test_scope():
for dtype in self._random_types():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
x = stateless.stateless_random_uniform(
shape=[1000], seed=seed_t, dtype=dtype)
y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
self.assertTrue(np.all(y >= 0))
self.assertTrue(np.all(y < 1))
def _chi_squared(self, x, bins):
"""Pearson's Chi-squared test."""
x = np.ravel(x)
n = len(x)
histogram, _ = np.histogram(x, bins=bins, range=(0, 1))
expected = n / float(bins)
return np.sum(np.square(histogram - expected) / expected)
def testDistributionOfStatelessRandomUniform(self):
"""Use Pearson's Chi-squared test to test for uniformity."""
with self.cached_session() as sess, self.test_scope():
for dtype in self._random_types():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
n = 1000
x = stateless.stateless_random_uniform(
shape=[n], seed=seed_t, dtype=dtype)
y = sess.run(x, {seed_t: [565656, 121212]})
# Tests that the values are distributed amongst 10 bins with equal
# probability. 16.92 is the Chi^2 value for 9 degrees of freedom with
# p=0.05. This test is probabilistic and would be flaky if the random
# seed were not fixed.
self.assertTrue(self._chi_squared(y, 10) < 16.92)
def testRandomNormalIsFinite(self):
with self.cached_session() as sess, self.test_scope():
for dtype in self._random_types():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
x = stateless.stateless_random_normal(
shape=[10000], seed=seed_t, dtype=dtype)
y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
self.assertTrue(np.all(np.isfinite(y)))
def _normal_cdf(self, x):
"""Cumulative distribution function for a standard normal distribution."""
return 0.5 + 0.5 * np.vectorize(math.erf)(x / math.sqrt(2))
def _anderson_darling(self, x):
"""Anderson-Darling test for a standard normal distribution."""
x = np.sort(np.ravel(x))
n = len(x)
i = np.linspace(1, n, n)
z = np.sum((2 * i - 1) * np.log(self._normal_cdf(x)) +
(2 * (n - i) + 1) * np.log(1 - self._normal_cdf(x)))
return -n - z / n
def testDistributionOfStatelessRandomNormal(self):
"""Use Anderson-Darling test to test distribution appears normal."""
with self.cached_session() as sess, self.test_scope():
for dtype in self._random_types():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
n = 1000
x = stateless.stateless_random_normal(
shape=[n], seed=seed_t, dtype=dtype)
y = sess.run(x, {seed_t: [25252, 314159]})
# The constant 2.492 is the 5% critical value for the Anderson-Darling
# test where the mean and variance are known. This test is probabilistic
# so to avoid flakiness the seed is fixed.
self.assertTrue(self._anderson_darling(y) < 2.492)
def testTruncatedNormalIsInRange(self):
for dtype in self._random_types():
with self.cached_session() as sess, self.test_scope():
seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
n = 10000000
x = stateless.stateless_truncated_normal(
shape=[n], seed=seed_t, dtype=dtype)
y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
def normal_cdf(x):
return .5 * math.erfc(-x / math.sqrt(2))
def normal_pdf(x):
return math.exp(-(x**2) / 2.) / math.sqrt(2 * math.pi)
def probit(x, sess=sess):
return sess.run(special_math.ndtri(x))
a = -2.
b = 2.
mu = 0.
sigma = 1.
alpha = (a - mu) / sigma
beta = (b - mu) / sigma
z = normal_cdf(beta) - normal_cdf(alpha)
self.assertTrue((y >= a).sum() == n)
self.assertTrue((y <= b).sum() == n)
# For more information on these calculations, see:
# Burkardt, John. "The Truncated Normal Distribution".
# Department of Scientific Computing website. Florida State University.
expected_mean = mu + (normal_pdf(alpha) - normal_pdf(beta)) / z * sigma
actual_mean = np.mean(y)
self.assertAllClose(actual_mean, expected_mean, atol=5e-4)
expected_median = mu + probit(
(normal_cdf(alpha) + normal_cdf(beta)) / 2.) * sigma
actual_median = np.median(y)
self.assertAllClose(actual_median, expected_median, atol=8e-4)
expected_variance = sigma**2 * (1 + (
(alpha * normal_pdf(alpha) - beta * normal_pdf(beta)) / z) - (
(normal_pdf(alpha) - normal_pdf(beta)) / z)**2)
actual_variance = np.var(y)
self.assertAllClose(actual_variance, expected_variance, rtol=1e-3)
if __name__ == '__main__':
test.main()
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