# Copyright 2017 The TensorFlow Authors. All Rights Reserved.
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#
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# Licensed under the Apache License, Version 2.0 (the "License");
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# you may not use this file except in compliance with the License.
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# You may obtain a copy of the License at
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#
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# http://www.apache.org/licenses/LICENSE-2.0
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#
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# Unless required by applicable law or agreed to in writing, software
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# distributed under the License is distributed on an "AS IS" BASIS,
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# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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# See the License for the specific language governing permissions and
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# limitations under the License.
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# ==============================================================================
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"""Tests for stateless random-number generation ops."""
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from __future__ import absolute_import
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from __future__ import division
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from __future__ import print_function
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import math
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import numpy as np
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from tensorflow.compiler.tests import xla_test
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from tensorflow.python.framework import dtypes
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from tensorflow.python.ops import array_ops
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from tensorflow.python.ops import stateless_random_ops as stateless
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from tensorflow.python.ops.distributions import special_math
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from tensorflow.python.platform import test
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class StatelessRandomOpsTest(xla_test.XLATestCase):
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"""Test cases for stateless random-number generator operators."""
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def _random_types(self, include_int=False):
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allowed_types = {dtypes.float32, dtypes.float64, dtypes.bfloat16}
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if include_int:
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allowed_types.update({dtypes.int32, dtypes.int64})
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return self.all_tf_types & allowed_types
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def testDeterminism(self):
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# Stateless values should be equal iff the seeds are equal (roughly)
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with self.cached_session(), self.test_scope():
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seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
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seeds = [(x, y) for x in range(5) for y in range(5)] * 3
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for stateless_op in [
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stateless.stateless_random_uniform, stateless.stateless_random_normal
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]:
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for shape in (), (3,), (2, 5):
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for dtype in self._random_types():
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# Skip bfloat16. The result of bfloat16 is truncated from 32-bit
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# result. With different seeds, the 32-bit results are different,
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# but the truncated 16-bit results might be the same.
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if dtype == dtypes.bfloat16:
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continue
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pure = stateless_op(shape, seed=seed_t, dtype=dtype)
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values = [(seed, pure.eval(feed_dict={
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seed_t: seed
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})) for seed in seeds]
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for s0, v0 in values:
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for s1, v1 in values:
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self.assertEqual(s0 == s1, np.all(v0 == v1))
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def testRandomUniformIsInRange(self):
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with self.cached_session() as sess, self.test_scope():
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for dtype in self._random_types(include_int=True):
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maxval = 1
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if dtype.is_integer:
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maxval = 100
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seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
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x = stateless.stateless_random_uniform(
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shape=[1000], seed=seed_t, maxval=maxval, dtype=dtype)
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y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
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self.assertTrue(np.all(y >= 0))
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self.assertTrue(np.all(y < maxval))
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def _chi_squared(self, x, bins):
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"""Pearson's Chi-squared test."""
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x = np.ravel(x)
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n = len(x)
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histogram, _ = np.histogram(x, bins=bins, range=(0, 1))
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expected = n / float(bins)
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return np.sum(np.square(histogram - expected) / expected)
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def testDistributionOfStatelessRandomUniform(self):
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"""Use Pearson's Chi-squared test to test for uniformity."""
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with self.cached_session() as sess, self.test_scope():
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for dtype in self._random_types(include_int=True):
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seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
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n = 1000
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maxval = 1
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if dtype.is_integer:
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maxval = 100
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x = stateless.stateless_random_uniform(
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shape=[n], seed=seed_t, maxval=maxval, dtype=dtype)
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y = sess.run(x, {seed_t: [565656, 121212]})
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if maxval > 1:
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# Normalize y to range [0, 1).
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y = y.astype(float) / maxval
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# Tests that the values are distributed amongst 10 bins with equal
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# probability. 16.92 is the Chi^2 value for 9 degrees of freedom with
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# p=0.05. This test is probabilistic and would be flaky if the random
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# seed were not fixed.
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self.assertTrue(self._chi_squared(y, 10) < 16.92)
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def testRandomNormalIsFinite(self):
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with self.cached_session() as sess, self.test_scope():
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for dtype in self._random_types():
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seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
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x = stateless.stateless_random_normal(
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shape=[10000], seed=seed_t, dtype=dtype)
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y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
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self.assertTrue(np.all(np.isfinite(y)))
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def _normal_cdf(self, x):
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"""Cumulative distribution function for a standard normal distribution."""
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return 0.5 + 0.5 * np.vectorize(math.erf)(x / math.sqrt(2))
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def _anderson_darling(self, x):
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"""Anderson-Darling test for a standard normal distribution."""
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x = np.sort(np.ravel(x))
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n = len(x)
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i = np.linspace(1, n, n)
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z = np.sum((2 * i - 1) * np.log(self._normal_cdf(x)) +
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(2 * (n - i) + 1) * np.log(1 - self._normal_cdf(x)))
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return -n - z / n
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def testDistributionOfStatelessRandomNormal(self):
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"""Use Anderson-Darling test to test distribution appears normal."""
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with self.cached_session() as sess, self.test_scope():
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for dtype in self._random_types():
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seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
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n = 1000
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x = stateless.stateless_random_normal(
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shape=[n], seed=seed_t, dtype=dtype)
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y = sess.run(x, {seed_t: [25252, 314159]})
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# The constant 2.492 is the 5% critical value for the Anderson-Darling
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# test where the mean and variance are known. This test is probabilistic
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# so to avoid flakiness the seed is fixed.
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self.assertTrue(self._anderson_darling(y.astype(float)) < 2.492)
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def testTruncatedNormalIsInRange(self):
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for dtype in self._random_types():
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with self.cached_session() as sess, self.test_scope():
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seed_t = array_ops.placeholder(dtypes.int32, shape=[2])
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n = 10000000
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x = stateless.stateless_truncated_normal(
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shape=[n], seed=seed_t, dtype=dtype)
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y = sess.run(x, {seed_t: [0x12345678, 0xabcdef12]})
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def normal_cdf(x):
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return .5 * math.erfc(-x / math.sqrt(2))
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def normal_pdf(x):
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return math.exp(-(x**2) / 2.) / math.sqrt(2 * math.pi)
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def probit(x, sess=sess):
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return self.evaluate(special_math.ndtri(x))
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a = -2.
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b = 2.
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mu = 0.
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sigma = 1.
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alpha = (a - mu) / sigma
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beta = (b - mu) / sigma
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z = normal_cdf(beta) - normal_cdf(alpha)
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self.assertEqual((y >= a).sum(), n)
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self.assertEqual((y <= b).sum(), n)
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# For more information on these calculations, see:
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# Burkardt, John. "The Truncated Normal Distribution".
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# Department of Scientific Computing website. Florida State University.
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expected_mean = mu + (normal_pdf(alpha) - normal_pdf(beta)) / z * sigma
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y = y.astype(float)
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actual_mean = np.mean(y)
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self.assertAllClose(actual_mean, expected_mean, atol=5e-4)
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expected_median = mu + probit(
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(normal_cdf(alpha) + normal_cdf(beta)) / 2.) * sigma
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actual_median = np.median(y)
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self.assertAllClose(actual_median, expected_median, atol=8e-4)
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expected_variance = sigma**2 * (1 + (
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(alpha * normal_pdf(alpha) - beta * normal_pdf(beta)) / z) - (
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(normal_pdf(alpha) - normal_pdf(beta)) / z)**2)
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actual_variance = np.var(y)
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self.assertAllClose(actual_variance, expected_variance,
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rtol=5e-3 if dtype == dtypes.bfloat16 else 1e-3)
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if __name__ == '__main__':
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test.main()
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