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random_test.py
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random_test.py
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# Copyright 2018 The JAX Authors.
#
# 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
#
# https://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.
import copy
import enum
from functools import partial
import math
from unittest import SkipTest, skipIf
from typing import Any, Tuple, NamedTuple, Optional
import zlib
from absl.testing import absltest
from absl.testing import parameterized
import numpy as np
import scipy.linalg
import scipy.special
import scipy.stats
import jax
from jax import grad
from jax import lax
from jax import numpy as jnp
from jax import prng
from jax import random
from jax import tree_util
from jax._src import core
from jax._src import dtypes
from jax._src import test_util as jtu
from jax import vmap
from jax.interpreters import xla
from jax._src import random as jax_random
from jax._src import prng as prng_internal
from jax import config
config.parse_flags_with_absl()
float_dtypes = jtu.dtypes.all_floating
complex_dtypes = jtu.dtypes.complex
int_dtypes = jtu.dtypes.all_integer
uint_dtypes = jtu.dtypes.all_unsigned
def _prng_key_as_array(key):
# TODO(frostig): remove once we upgrade to always enable_custom_prng
return key.unsafe_raw_array() if config.jax_enable_custom_prng else key
def _maybe_unwrap(key):
# TODO(frostig): remove once we upgrade to always enable_custom_prng
unwrap = prng_internal.random_unwrap
return unwrap(key) if config.jax_enable_custom_prng else key
PRNG_IMPLS = [('threefry2x32', prng.threefry_prng_impl),
('rbg', prng.rbg_prng_impl),
('unsafe_rbg', prng.unsafe_rbg_prng_impl)]
class OnX64(enum.Enum):
ALSO = enum.auto()
SKIP = enum.auto()
ONLY = enum.auto()
class RandomValuesCase(NamedTuple):
name: str
prng_impl: str
shape: Tuple[int, ...]
dtype: Any
params: dict
expected: np.ndarray
on_x64: OnX64 = OnX64.ALSO
atol: Optional[float] = None
rtol: Optional[float] = None
def _testname(self):
if self.dtype is None:
shape_dtype = str(self.shape)
else:
shape_dtype = jtu.format_shape_dtype_string(self.shape, self.dtype)
name = f"_{self.name}_{self.prng_impl}_{shape_dtype}"
if self.params:
fmt = lambda x: str(x).replace(' ', '').replace('\n', '')
name += "_" + "_".join(f"{k}={fmt(v)}" for k, v in self.params.items())
return name
def _seed(self):
# Generate a deterministic unique 32-bit seed given the name and prng impl
return zlib.adler32((self.name + self.prng_impl).encode())
_RANDOM_VALUES_CASES = [
# TODO(jakevdp) add coverage for other distributions.
RandomValuesCase("bernoulli", "threefry2x32", (5,), None, {'p': 0.5},
np.array([False, True, True, True, False]), on_x64=OnX64.SKIP),
RandomValuesCase("bernoulli", "rbg", (5,), None, {'p': 0.5},
np.array([True, True, True, True, True]), on_x64=OnX64.SKIP),
RandomValuesCase("beta", "threefry2x32", (5,), np.float32, {'a': 0.8, 'b': 0.9},
np.array([0.533685, 0.843179, 0.063495, 0.573444, 0.459514], dtype='float32')),
RandomValuesCase("beta", "rbg", (5,), np.float32, {'a': 0.8, 'b': 0.9},
np.array([0.841308, 0.669989, 0.731763, 0.985127, 0.022745], dtype='float32')),
# TODO(frostig,jakevdp) add coverage for non-threefry bits
RandomValuesCase("bits", "threefry2x32", (5,), np.uint8, {},
np.array([10, 158, 82, 54, 158], dtype='uint8')),
RandomValuesCase("bits", "threefry2x32", (5,), np.uint16, {},
np.array([6738, 38161, 50695, 57337, 61600], dtype='uint16')),
RandomValuesCase("bits", "threefry2x32", (5,), np.uint32, {},
np.array([1978747883, 4134381225, 3628107870, 689687174, 2788938207], dtype='uint32')),
RandomValuesCase("bits", "threefry2x32", (5,), np.uint64, {},
np.array([17649965731882839947, 1415307058040849897, 8282622628079774249,
14024425113645909402, 2012979996110532418], dtype='uint64'),
on_x64=OnX64.ONLY),
RandomValuesCase("cauchy", "threefry2x32", (5,), np.float32, {},
np.array([ -0.088416, -10.169713, 3.49677, -1.18056, 0.34556], dtype='float32'), rtol=1E-5),
RandomValuesCase("cauchy", "rbg", (5,), np.float32, {},
np.array([0.008389, 0.108793, -0.031826, -0.01876, 0.963218], dtype='float32')),
RandomValuesCase("dirichlet", "threefry2x32", (2,), np.float32, {'alpha': np.array([0.5, 0.6, 0.7], dtype='float32')},
np.array([[0.556287, 0.304219, 0.139494], [0.15221 , 0.632251, 0.21554]], dtype='float32')),
RandomValuesCase("dirichlet", "rbg", (2,), np.float32, {'alpha': np.array([0.5, 0.6, 0.7], dtype='float32')},
np.array([[0.024769, 0.002189, 0.973041], [0.326, 0.00244, 0.67156]], dtype='float32')),
RandomValuesCase("double_sided_maxwell", "threefry2x32", (5,), np.float32, {"loc": 1, "scale": 2},
np.array([-2.408914, -3.370437, 3.235352, -0.907734, -1.708732], dtype='float32'), on_x64=OnX64.SKIP),
RandomValuesCase("double_sided_maxwell", "rbg", (5,), np.float32, {"loc": 1, "scale": 2},
np.array([4.957495, 3.003086, 5.33935, 2.942878, -1.203524], dtype='float32'), on_x64=OnX64.SKIP),
RandomValuesCase("exponential", "threefry2x32", (5,), np.float32, {},
np.array([0.526067, 0.043046, 0.039932, 0.46427 , 0.123886], dtype='float32')),
RandomValuesCase("exponential", "rbg", (5,), np.float32, {},
np.array([0.231303, 0.684814, 0.017181, 0.089552, 0.345087], dtype='float32')),
RandomValuesCase("gamma", "threefry2x32", (5,), np.float32, {'a': 0.8},
np.array([0.332641, 0.10187 , 1.816109, 0.023457, 0.487853], dtype='float32')),
RandomValuesCase("gamma", "rbg", (5,), np.float32, {'a': 0.8},
np.array([0.235293, 0.446747, 0.146372, 0.79252 , 0.294762], dtype='float32')),
RandomValuesCase("gumbel", "threefry2x32", (5,), np.float32, {},
np.array([2.06701, 0.911726, 0.145736, 0.185427, -0.00711], dtype='float32')),
RandomValuesCase("gumbel", "rbg", (5,), np.float32, {},
np.array([-0.099308, -1.123809, 1.007618, -0.077968, 3.421349], dtype='float32')),
RandomValuesCase("laplace", "threefry2x32", (5,), np.float32, {},
np.array([0.578939, -0.204902, 0.555733, 0.911053, -0.96456], dtype='float32')),
RandomValuesCase("laplace", "rbg", (5,), np.float32, {},
np.array([-2.970422, 1.925082, -0.757887, -4.444797, 0.561983], dtype='float32')),
RandomValuesCase("loggamma", "threefry2x32", (5,), np.float32, {'a': 0.8},
np.array([-0.899633, -0.424083, 0.631593, 0.102374, -1.07189], dtype='float32')),
RandomValuesCase("loggamma", "rbg", (5,), np.float32, {'a': 0.8},
np.array([-1.333825, 0.287259, -0.343074, -0.998258, -0.773598], dtype='float32')),
RandomValuesCase("logistic", "threefry2x32", (5,), np.float32, {},
np.array([0.19611, -1.709053, -0.274093, -0.208322, -1.675489], dtype='float32')),
RandomValuesCase("logistic", "rbg", (5,), np.float32, {},
np.array([-0.234923, -0.545184, 0.700992, -0.708609, -1.474884], dtype='float32')),
RandomValuesCase("maxwell", "threefry2x32", (5,), np.float32, {},
np.array([3.070779, 0.908479, 1.521317, 0.875551, 1.306137], dtype='float32')),
RandomValuesCase("maxwell", "rbg", (5,), np.float32, {},
np.array([2.048746, 0.470027, 1.053105, 1.01969, 2.710645], dtype='float32')),
RandomValuesCase("multivariate_normal", "threefry2x32", (2,), np.float32, {"mean": np.ones((1, 3)), "cov": np.eye(3)},
np.array([[ 1.067826, 1.215599, 0.234166], [-0.237534, 1.32591, 1.413987]], dtype='float32'), on_x64=OnX64.SKIP),
RandomValuesCase("multivariate_normal", "rbg", (2,), np.float32, {"mean": np.ones((1, 3)), "cov": np.eye(3)},
np.array([[-0.036897, 0.770969, 0.756959], [1.755091, 2.350553, 0.627142]], dtype='float32'), on_x64=OnX64.SKIP),
RandomValuesCase("normal", "threefry2x32", (5,), np.float32, {},
np.array([-1.173234, -1.511662, 0.070593, -0.099764, 1.052845], dtype='float32')),
RandomValuesCase("normal", "rbg", (5,), np.float32, {},
np.array([-0.479658, 0.565747, -1.065106, 0.997962, -1.478002], dtype='float32')),
RandomValuesCase("pareto", "threefry2x32", (5,), np.float32, {"b": 0.5},
np.array([2.751398, 1.281863, 87.85448, 1.254542, 2.824487], dtype='float32')),
RandomValuesCase("pareto", "rbg", (5,), np.float32, {"b": 0.5},
np.array([1.241914, 1.521864, 5.615384, 1911.502, 1.816702], dtype='float32')),
RandomValuesCase("poisson", "threefry2x32", (5,), np.int32, {"lam": 5},
np.array([7, 3, 6, 11, 6], dtype='int32')),
# Note: poisson not implemented for rbg sampler.
RandomValuesCase("rademacher", "threefry2x32", (5,), np.int32, {},
np.array([-1, -1, -1, -1, 1], dtype='int32'), on_x64=OnX64.SKIP),
RandomValuesCase("rademacher", "rbg", (5,), np.int32, {},
np.array([1, 1, 1, -1, -1], dtype='int32'), on_x64=OnX64.SKIP),
RandomValuesCase("randint", "threefry2x32", (5,), np.int32, {"minval": 0, "maxval": 10},
np.array([0, 5, 7, 7, 5], dtype='int32')),
RandomValuesCase("randint", "rbg", (5,), np.int32, {"minval": 0, "maxval": 10},
np.array([7, 1, 8, 5, 8], dtype='int32')),
RandomValuesCase("truncated_normal", "threefry2x32", (5,), np.float32, {"lower": 0, "upper": 2},
np.array([0.582807, 1.709771, 0.159513, 0.861376, 0.36148], dtype='float32')),
RandomValuesCase("truncated_normal", "rbg", (5,), np.float32, {"lower": 0, "upper": 2},
np.array([0.770068, 1.516464, 0.710406, 0.762801, 1.305324], dtype='float32')),
RandomValuesCase("uniform", "threefry2x32", (5,), np.float32, {},
np.array([0.298671, 0.073213, 0.873356, 0.260549, 0.412797], dtype='float32')),
RandomValuesCase("uniform", "rbg", (5,), np.float32, {},
np.array([0.477161, 0.706508, 0.656261, 0.432547, 0.057772], dtype='float32')),
RandomValuesCase("weibull_min", "threefry2x32", (5,), np.float32, {"scale": 1, "concentration": 1},
np.array([1.605863, 0.841809, 0.224218, 0.4826 , 0.027901], dtype='float32')),
RandomValuesCase("weibull_min", "rbg", (5,), np.float32, {"scale": 1, "concentration": 1},
np.array([1.370903, 0.086532, 0.061688, 3.407599, 0.215077], dtype='float32')),
]
class PrngTest(jtu.JaxTestCase):
def testThreefry2x32(self):
# We test the hash by comparing to known values provided in the test code of
# the original reference implementation of Threefry. For the values, see
# https://github.com/DEShawResearch/Random123-Boost/blob/65e3d874b67aa7b3e02d5ad8306462f52d2079c0/libs/random/test/test_threefry.cpp#L30-L32
def result_to_hex(result):
return tuple(hex(x.copy()).rstrip("L") for x in result)
expected = ("0x6b200159", "0x99ba4efe")
result = prng.threefry_2x32(np.uint32([0, 0]), np.uint32([0, 0]))
self.assertEqual(expected, result_to_hex(result))
expected = ("0x1cb996fc", "0xbb002be7")
u32_max = np.iinfo(np.uint32).max
result = prng.threefry_2x32(np.uint32([u32_max, u32_max]), np.uint32([u32_max, u32_max]))
self.assertEqual(expected, result_to_hex(result))
expected = ("0xc4923a9c", "0x483df7a0")
result = prng.threefry_2x32(
np.uint32([0x13198a2e, 0x03707344]),
np.uint32([0x243f6a88, 0x85a308d3]))
self.assertEqual(expected, result_to_hex(result))
def testThreefry2x32Large(self):
n = 10000000
result = prng.threefry_2x32(
(np.uint32(0x13198a2e), np.uint32(0x03707344)),
jnp.concatenate([
jnp.full((n,), 0x243f6a88, jnp.uint32),
jnp.full((n,), 0x85a308d3, jnp.uint32)
]))
np.testing.assert_equal(result[:n], np.full((n,), 0xc4923a9c, dtype=np.uint32))
np.testing.assert_equal(result[n:], np.full((n,), 0x483df7a0, dtype=np.uint32))
def testThreefry2x32Empty(self):
# Regression test for an op-by-op crash for empty arrays in CUDA mode.
with jax.disable_jit():
result = prng.threefry_2x32(
(np.uint32(0x13198a2e), np.uint32(0x03707344)),
jnp.ones((10, 0,), jnp.uint32))
np.testing.assert_equal(result, np.zeros((10, 0,), dtype=np.uint32))
def testNoOpByOpUnderHash(self):
def fail(*args, **kwargs): assert False
apply_primitive, xla.apply_primitive = xla.apply_primitive, fail
try:
_ = prng.threefry_2x32(np.zeros(2, np.uint32), np.arange(10, dtype=np.uint32))
finally:
xla.apply_primitive = apply_primitive
@skipIf(config.jax_threefry_partitionable, 'changed random bit values')
def testRngRandomBits(self):
# Test specific outputs to ensure consistent random values between JAX versions.
# TODO(frostig): remove once we always enable_custom_prng
def random_bits(key, *args):
key, _ = jax_random._check_prng_key(key)
return jax_random._random_bits(key, *args)
key = random.PRNGKey(1701)
bits8 = random_bits(key, 8, (3,))
expected8 = np.array([216, 115, 43], dtype=np.uint8)
self.assertArraysEqual(bits8, expected8)
bits16 = random_bits(key, 16, (3,))
expected16 = np.array([41682, 1300, 55017], dtype=np.uint16)
self.assertArraysEqual(bits16, expected16)
bits32 = random_bits(key, 32, (3,))
expected32 = np.array([56197195, 4200222568, 961309823], dtype=np.uint32)
self.assertArraysEqual(bits32, expected32)
with jtu.ignore_warning(category=UserWarning, message="Explicitly requested dtype.*"):
bits64 = random_bits(key, 64, (3,))
if config.x64_enabled:
expected64 = np.array([3982329540505020460, 16822122385914693683,
7882654074788531506], dtype=np.uint64)
else:
expected64 = np.array([676898860, 3164047411, 4010691890], dtype=np.uint32)
self.assertArraysEqual(bits64, expected64)
@jtu.sample_product(prng_name=[name for name, _ in PRNG_IMPLS])
def testRngRandomBitsShapeDtype(self, prng_name):
# Like testRngRandomBits, but only meant to exercise random_bits
# on every PRNG implementation. Instead of values, only checks
# that shapes/dtypes are as expected.
# TODO(frostig): remove once we always enable_custom_prng
def random_bits(key, *args):
key, _ = jax_random._check_prng_key(key)
return jax_random._random_bits(key, *args)
with jax.default_prng_impl(prng_name):
key = random.PRNGKey(1701)
bits8 = random_bits(key, 8, (3,))
self.assertEqual(bits8.shape, (3,))
self.assertEqual(bits8.dtype, np.dtype('uint8'))
bits16 = random_bits(key, 16, (3,))
self.assertEqual(bits16.shape, (3,))
self.assertEqual(bits16.dtype, np.dtype('uint16'))
bits32 = random_bits(key, 32, (3,))
self.assertEqual(bits32.shape, (3,))
self.assertEqual(bits32.dtype, np.dtype('uint32'))
with jtu.ignore_warning(category=UserWarning, message="Explicitly requested dtype.*"):
bits64 = random_bits(key, 64, (3,))
expected_dtype = np.dtype('uint64' if config.x64_enabled else 'uint32')
self.assertEqual(bits64.shape, (3,))
self.assertEqual(bits64.dtype, expected_dtype)
@skipIf(config.jax_threefry_partitionable, 'changed random bit values')
def testRngRandomBitsViewProperty(self):
# TODO: add 64-bit if it ever supports this property.
# TODO: will this property hold across endian-ness?
# TODO(frostig): remove once we always enable_custom_prng
def random_bits(key, *args):
key, _ = jax_random._check_prng_key(key)
return jax_random._random_bits(key, *args)
N = 10
key = random.PRNGKey(1701)
nbits = [8, 16, 32]
rand_bits = [random_bits(key, n, (N * 64 // n,)) for n in nbits]
rand_bits_32 = np.array([np.array(r).view(np.uint32) for r in rand_bits])
assert np.all(rand_bits_32 == rand_bits_32[0])
@jtu.sample_product(case=_RANDOM_VALUES_CASES)
@skipIf(config.jax_threefry_partitionable, 'changed random bit values')
@jtu.skip_on_devices("tpu") # TPU precision causes issues.
def testRandomDistributionValues(self, case):
"""
Tests values output by various distributions. This will catch any unintentional
changes to the implementations that could result in different random sequences.
Any refactoring of random distributions that leads to non-trivial differences in
this test should involve a deprecation cycle following the procedures outlined at
https://jax.readthedocs.io/en/latest/api_compatibility.html
"""
if config.x64_enabled and case.on_x64 == OnX64.SKIP:
self.skipTest("test produces different values when jax_enable_x64=True")
if not config.x64_enabled and case.on_x64 == OnX64.ONLY:
self.skipTest("test only valid when jax_enable_x64=True")
with jax.default_prng_impl(case.prng_impl):
func = getattr(random, case.name)
key = random.PRNGKey(case._seed())
if case.dtype:
actual = func(key, **case.params, shape=case.shape, dtype=case.dtype)
else:
actual = func(key, **case.params, shape=case.shape)
self.assertAllClose(actual, case.expected, atol=case.atol, rtol=case.rtol)
@skipIf(config.jax_threefry_partitionable, 'changed random bit values')
def testPRNGValues(self):
# Test to ensure consistent random values between JAX versions
k = random.PRNGKey(0)
self.assertEqual(random.randint(k, (3, 3), 0, 8).dtype,
dtypes.canonicalize_dtype(jnp.int_))
if config.x64_enabled:
self.assertAllClose(
random.randint(k, (3, 3), 0, 8, dtype='int64'),
np.array([[7, 2, 6],
[2, 1, 0],
[6, 7, 7]], dtype='int64'))
self.assertAllClose(
random.randint(k, (3, 3), 0, 8, dtype='int32'),
np.array([[2, 1, 3],
[6, 1, 5],
[6, 3, 4]], dtype='int32'))
self.assertAllClose(
_prng_key_as_array(random.split(k, 4)),
np.array([[2285895361, 1501764800],
[1518642379, 4090693311],
[ 433833334, 4221794875],
[ 839183663, 3740430601]], dtype='uint32'))
self.assertAllClose(
_prng_key_as_array(random.fold_in(k, 4)),
np.array([2285895361, 433833334], dtype='uint32'))
def test_random_bits_error(self):
msg = 'dtype argument .* must be an unsigned int dtype'
with self.assertRaisesRegex(ValueError, msg):
random.bits(random.PRNGKey(0), (3, 4), np.dtype('int8'))
with self.assertRaisesRegex(ValueError, msg):
random.bits(random.PRNGKey(0), (3, 4), np.dtype('float16'))
@skipIf(not config.jax_threefry_partitionable, 'enable after upgrade')
def test_threefry_split_fold_in_symmetry(self):
with jax.default_prng_impl('threefry2x32'):
key = random.PRNGKey(72)
f1, f2, f3 = [random.fold_in(key, i) for i in range(3)]
s1, s2, s3 = random.split(key, 3)
f1, f2, f3 = map(_prng_key_as_array, [f1, f2, f3])
s1, s2, s3 = map(_prng_key_as_array, [s1, s2, s3])
self.assertArraysEqual(f1, s1)
self.assertArraysEqual(f2, s2)
self.assertArraysEqual(f3, s3)
@skipIf(not config.jax_threefry_partitionable, 'enable after upgrade')
def test_threefry_split_vmapped_fold_in_symmetry(self):
# See https://github.com/google/jax/issues/7708
with jax.default_prng_impl('threefry2x32'):
key = random.PRNGKey(72)
f1, f2, f3 = vmap(lambda k, _: random.fold_in(k, lax.axis_index('batch')),
in_axes=(None, 0), axis_name='batch')(key, jnp.ones(3))
s1, s2, s3 = random.split(key, 3)
f1, f2, f3 = map(_prng_key_as_array, [f1, f2, f3])
s1, s2, s3 = map(_prng_key_as_array, [s1, s2, s3])
self.assertArraysEqual(f1, s1)
self.assertArraysEqual(f2, s2)
self.assertArraysEqual(f3, s3)
@parameterized.parameters([
{"seed": 0, "typ": int, "jit": True, "key": [0, 0]},
{"seed": 0, "typ": int, "jit": False, "key": [0, 0]},
{"seed": 1, "typ": np.int32, "jit": True, "key": [0, 1]},
{"seed": 1, "typ": np.int32, "jit": False, "key": [0, 1]},
{"seed": 2, "typ": np.uint32, "jit": True, "key": [0, 2]},
{"seed": 2, "typ": np.uint32, "jit": False, "key": [0, 2]},
{"seed": 3, "typ": np.int64, "jit": True, "key": [0, 3]},
{"seed": 3, "typ": np.int64, "jit": False, "key": [0, 3]},
{"seed": -1, "typ": int, "jit": True, "key": [4294967295, 4294967295] if config.x64_enabled else [0, 4294967295]},
{"seed": -1, "typ": int, "jit": False, "key": [4294967295, 4294967295] if config.x64_enabled else [0, 4294967295]},
{"seed": -2, "typ": np.int32, "jit": True, "key": [0, 4294967294]},
{"seed": -2, "typ": np.int32, "jit": False, "key": [0, 4294967294]},
{"seed": -3, "typ": np.int64, "jit": True, "key": [4294967295, 4294967293] if config.x64_enabled else [0, 4294967293]},
{"seed": -3, "typ": np.int64, "jit": False, "key": [4294967295, 4294967293] if config.x64_enabled else [0, 4294967293]},
{"seed": np.iinfo(np.int32).max + 100, "typ": int, "jit": True, "key": [0, 2147483747]},
{"seed": np.iinfo(np.int32).max + 100, "typ": int, "jit": False, "key": [0, 2147483747]},
{"seed": np.iinfo(np.int32).max + 101, "typ": np.uint32, "jit": True, "key": [0, 2147483748]},
{"seed": np.iinfo(np.int32).max + 101, "typ": np.uint32, "jit": False, "key": [0, 2147483748]},
{"seed": np.iinfo(np.int32).min - 100, "typ": int, "jit": True, "key": [4294967295, 2147483548] if config.x64_enabled else [0, 2147483548]},
{"seed": np.iinfo(np.int32).min - 100, "typ": int, "jit": False, "key": [4294967295, 2147483548] if config.x64_enabled else [0, 2147483548]},
{"seed": np.iinfo(np.int32).min - 101, "typ": np.int64, "jit": True, "key": [4294967295, 2147483547] if config.x64_enabled else [0, 2147483547]},
{"seed": np.iinfo(np.int32).min - 101, "typ": np.int64, "jit": False, "key": [4294967295, 2147483547] if config.x64_enabled else [0, 2147483547]},
])
def test_prng_seeds_and_keys(self, seed, typ, jit, key):
seed = typ(seed)
if jit:
maker = lambda k: _prng_key_as_array(jax.jit(random.PRNGKey)(k))
else:
maker = lambda k: _prng_key_as_array(random.PRNGKey(k))
if (jit and typ is int and not config.x64_enabled and
(seed < np.iinfo('int32').min or seed > np.iinfo('int32').max)):
# We expect an error to be raised.
# NOTE: we check 'if jit' because some people rely on builtin int seeds
# (e.g. from PRNGKey(hash("altair is best plotting library"))) outside jit
# First check with no cache entry (note lambda above).
with self.assertRaises(OverflowError):
maker(seed)
# Then populate a cache entry.
maker(typ(0)).block_until_ready()
# Then check now that we have a cache entry.
with self.assertRaises(OverflowError):
maker(seed)
else:
# Otherwise we expect no error.
actual = maker(seed)
expected = jnp.array(key, dtype=jnp.uint32)
self.assertArraysEqual(actual, expected)
def test_default_prng_selection(self):
if not config.jax_enable_custom_prng:
self.skipTest("test requires config.jax_enable_custom_prng")
for name, impl in PRNG_IMPLS:
with jax.default_prng_impl(name):
self.assertIs(random.default_prng_impl(), impl)
key = random.PRNGKey(42)
self.assertIs(key.impl, impl)
k1, k2 = random.split(key, 2)
self.assertIs(k1.impl, impl)
self.assertIs(k2.impl, impl)
def test_default_prng_selection_without_custom_prng_mode(self):
if config.jax_enable_custom_prng:
self.skipTest("test requires that config.jax_enable_custom_prng is False")
for name, impl in PRNG_IMPLS:
with jax.default_prng_impl(name):
self.assertIs(random.default_prng_impl(), impl)
key = random.PRNGKey(42)
self.assertEqual(key.shape, impl.key_shape)
k1, k2 = random.split(key, 2)
self.assertEqual(k1.shape, impl.key_shape)
self.assertEqual(k2.shape, impl.key_shape)
def test_explicit_threefry2x32_key(self):
if not config.jax_enable_custom_prng:
self.skipTest("test requires config.jax_enable_custom_prng")
key = random.threefry2x32_key(42)
self.assertIs(key.impl, prng.threefry_prng_impl)
def test_explicit_rbg_key(self):
if not config.jax_enable_custom_prng:
self.skipTest("test requires config.jax_enable_custom_prng")
key = random.rbg_key(42)
self.assertIs(key.impl, prng.rbg_prng_impl)
def test_explicit_unsafe_rbg_key(self):
if not config.jax_enable_custom_prng:
self.skipTest("test requires config.jax_enable_custom_prng")
key = random.unsafe_rbg_key(42)
self.assertIs(key.impl, prng.unsafe_rbg_prng_impl)
def test_key_array_indexing_0d(self):
if not config.jax_enable_custom_prng:
self.skipTest("test requires config.jax_enable_custom_prng")
key = random.PRNGKey(1701)
self.assertEqual(key.shape, ())
self.assertEqual(key[None].shape, (1,))
self.assertRaisesRegex(IndexError, 'Too many indices.*', lambda: key[0])
def test_key_array_indexing_nd(self):
if not config.jax_enable_custom_prng:
self.skipTest("test requires config.jax_enable_custom_prng")
keys = vmap(vmap(random.PRNGKey))(jnp.arange(6).reshape((2, 3)))
self.assertEqual(keys.shape, (2, 3))
self.assertEqual(keys[0, 0].shape, ())
self.assertEqual(keys[0, 1].shape, ())
self.assertEqual(keys[0].shape, (3,))
self.assertEqual(keys[1, :].shape, (3,))
self.assertEqual(keys[:, 1].shape, (2,))
self.assertEqual(keys[None].shape, (1, 2, 3))
self.assertEqual(keys[None, None].shape, (1, 1, 2, 3))
self.assertEqual(keys[None, :, None].shape, (1, 2, 1, 3))
self.assertEqual(keys[None, None, None, 0, None, None, None, 1].shape,
(1,) * 6)
self.assertEqual(keys[..., 1:, None].shape, (2, 2, 1))
self.assertEqual(keys[None, 0, ..., 1, None].shape, (1, 1))
self.assertRaisesRegex(IndexError, 'Too many indices.*',
lambda: keys[0, 1, 2])
self.assertRaisesRegex(IndexError, 'Too many indices.*',
lambda: keys[0, 1, None, 2])
def test_isinstance(self):
if not config.jax_enable_custom_prng:
self.skipTest("test requires config.jax_enable_custom_prng")
key = random.PRNGKey(0)
self.assertIsInstance(key, jax.Array)
def test_key_output_vjp(self):
# See https://github.com/google/jax/issues/14856
def f(seed): return random.PRNGKey(seed)
jax.vjp(f, 1) # doesn't crash
class ThreefryPrngTest(jtu.JaxTestCase):
def test_seed_no_implicit_transfers(self):
# See https://github.com/google/jax/issues/15613
with jax.transfer_guard('disallow'):
random.threefry2x32_key(jax.device_put(42)) # doesn't crash
class LaxRandomTest(jtu.JaxTestCase):
def _CheckCollisions(self, samples, nbits):
fail_prob = 0.01 # conservative bound on statistical fail prob by Chebyshev
nitems = len(samples)
nbins = 2 ** nbits
nexpected = nbins * (1 - ((nbins - 1) / nbins) ** nitems)
ncollisions = len(np.unique(samples))
sq_percent_deviation = ((ncollisions - nexpected) / nexpected) ** 2
self.assertLess(sq_percent_deviation, 1 / np.sqrt(nexpected * fail_prob))
def _CheckKolmogorovSmirnovCDF(self, samples, cdf):
# conservative bound on statistical fail prob by Kolmo CDF
# bfloat16 quantization creates much lower p-values in large distributions
fail_prob = 0.003 if samples.dtype == jnp.bfloat16 else 0.01
if config.jax_enable_custom_prng and samples.dtype == jnp.bfloat16:
return
self.assertGreater(scipy.stats.kstest(samples, cdf).pvalue, fail_prob)
def _CheckChiSquared(self, samples, pmf):
if samples.dtype == bool:
samples = samples.astype(int)
alpha = 0.01 # significance level, threshold for p-value
# scipy.stats.chisquare requires the sum of expected and actual to
# match; this is only the case if we compute the expected frequency
# at *all* nonzero values of the pmf. We don't know this a priori,
# so we add extra values past the largest observed value. The number
# below is empirically enough to get full coverage for the current set
# of tests. If a new test is added where this is not enough, chisquare()
# below will error due to the sums of the inputs not matching.
extra_values = 100
actual_freq = np.bincount(samples, minlength=samples.max() + extra_values)
values = np.arange(len(actual_freq))
expected_freq = pmf(values) * samples.size
valid = expected_freq > 0
actual_freq = actual_freq[valid]
expected_freq = expected_freq[valid]
_, p_value = scipy.stats.chisquare(actual_freq, expected_freq)
self.assertGreater(
p_value, alpha,
msg=f'Failed chi-squared test with p={p_value}.\n'
'Expected vs. actual frequencies:\n'
f'{expected_freq}\n{actual_freq}')
def seed_prng(self, seed):
return random.threefry2x32_key(seed)
@jtu.sample_product(dtype=jtu.dtypes.floating)
def testNumpyAndXLAAgreeOnFloatEndianness(self, dtype):
bits_dtype = np.uint32 if jnp.finfo(dtype).bits == 32 else np.uint64
numpy_bits = np.array(1., dtype).view(bits_dtype)
xla_bits = jax.jit(
lambda: lax.bitcast_convert_type(np.array(1., dtype), bits_dtype))()
self.assertEqual(numpy_bits, xla_bits)
@jtu.sample_product(dtype=float_dtypes)
def testRngUniform(self, dtype):
key = self.seed_prng(0)
rand = lambda key: random.uniform(key, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key)
compiled_samples = crand(key)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckCollisions(samples, jnp.finfo(dtype).nmant)
self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.uniform().cdf)
@jtu.sample_product(dtype=int_dtypes + uint_dtypes)
def testRngRandint(self, dtype):
lo = 5
hi = 10
key = self.seed_prng(0)
rand = lambda key: random.randint(key, (10000,), lo, hi, dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key)
compiled_samples = crand(key)
for samples in [uncompiled_samples, compiled_samples]:
self.assertTrue(np.all(lo <= samples))
self.assertTrue(np.all(samples < hi))
@jtu.sample_product(dtype=float_dtypes)
def testNormal(self, dtype):
key = self.seed_prng(0)
rand = lambda key: random.normal(key, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key)
compiled_samples = crand(key)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.norm().cdf)
def testNormalBfloat16(self):
# Passing bfloat16 as dtype string.
# https://github.com/google/jax/issues/6813
res_bfloat16_str = random.normal(self.seed_prng(0), dtype='bfloat16')
res_bfloat16 = random.normal(self.seed_prng(0), dtype=jnp.bfloat16)
self.assertAllClose(res_bfloat16, res_bfloat16_str)
@jtu.sample_product(dtype=complex_dtypes)
def testNormalComplex(self, dtype):
key = self.seed_prng(0)
rand = lambda key: random.normal(key, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key)
compiled_samples = crand(key)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(jnp.real(samples), scipy.stats.norm(scale=1/np.sqrt(2)).cdf)
self._CheckKolmogorovSmirnovCDF(jnp.imag(samples), scipy.stats.norm(scale=1/np.sqrt(2)).cdf)
self.assertEqual(dtype, samples.dtype)
@jtu.sample_product(dtype=float_dtypes)
def testTruncatedNormal(self, dtype):
key = self.seed_prng(0)
rand = lambda key: random.truncated_normal(key, -0.3, 0.3, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key)
compiled_samples = crand(key)
min_val = np.min(uncompiled_samples)
max_val = np.max(uncompiled_samples)
self.assertTrue(min_val > -0.3)
self.assertTrue(max_val < 0.3)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.truncnorm(-0.3, 0.3).cdf)
@jtu.sample_product(dtype=jtu.dtypes.floating + jtu.dtypes.integer)
def testShuffle(self, dtype):
key = self.seed_prng(0)
x = np.arange(100).astype(dtype)
rand = lambda key: random.shuffle(key, x)
crand = jax.jit(rand)
with self.assertWarns(FutureWarning):
perm1 = rand(key)
with self.assertWarns(FutureWarning):
perm2 = crand(key)
self.assertAllClose(perm1, perm2)
self.assertFalse(np.all(perm1 == x)) # seems unlikely!
self.assertAllClose(np.sort(perm1), x, check_dtypes=False)
@jtu.sample_product(
[dict(shape=shape, replace=replace, axis=axis,
input_range_or_shape=input_range_or_shape)
for shape in [(), (5,), (4, 5)]
for replace in [True, False]
for input_range_or_shape in [100, (10, 10), (10, 5, 2), 1, (1, 5)]
for is_range in [type(input_range_or_shape) is int]
for ndim in [1 if is_range else len(input_range_or_shape)]
for axis in range(-ndim, ndim or 1)
for ninputs in [input_range_or_shape if is_range else input_range_or_shape[axis]]
if replace or math.prod(shape) <= ninputs
],
dtype=jtu.dtypes.floating + jtu.dtypes.integer,
weighted=[True, False],
)
def testChoice(self, dtype, input_range_or_shape, shape, replace, weighted, axis):
# This is the function API that we test against (note that self.rng().choice differs)
np_choice = np.random.default_rng(0).choice
p_dtype = dtypes.to_inexact_dtype(dtype)
key = self.seed_prng(0)
is_range = type(input_range_or_shape) is int
x = (input_range_or_shape if is_range else
self.rng().permutation(np.arange(math.prod(
input_range_or_shape), dtype=dtype)).reshape(input_range_or_shape))
N = x if is_range else x.shape[axis]
if weighted:
p = np.arange(N, dtype=p_dtype) + 1
p /= p.sum()
else:
p = None
rand = lambda key, x: random.choice(key, x, shape, replace, p, axis)
sample = rand(key, x)
if not is_range:
self.assertEqual(dtype, sample.dtype)
expected_shape = np.shape(np_choice(x, shape or None, replace, p, axis))
self.assertEqual(expected_shape, sample.shape)
expected_dtype = dtypes.result_type(int if is_range else x)
self.assertEqual(expected_dtype, sample.dtype)
if not replace and shape:
def lsort(x):
if not math.prod(x.shape): return x
ind = np.lexsort(np.swapaxes(x, axis, -1).reshape((-1, x.shape[axis])))
return jnp.take(x, ind, axis)
self.assertArraysEqual(lsort(sample), lsort(np.unique(sample, axis=axis)))
self.assertArraysEqual(sample, rand(key, np.array(x)))
self.assertArraysEqual(sample, jax.jit(rand, static_argnames=
'x' if is_range else None)(key, x))
@jtu.sample_product(
[dict(range_or_shape=range_or_shape, axis=axis)
for range_or_shape in [0, 1, 100, (0,), (1,), (100,),
(10, 10), (10, 5, 2), (0, 5), (1, 5)]
for ndim in [1 if type(range_or_shape) is int else len(range_or_shape)]
for axis in range(-ndim, ndim or 1)
],
dtype=jtu.dtypes.floating + jtu.dtypes.integer,
independent=[True, False],
)
def testPermutation(self, dtype, range_or_shape, axis, independent):
key = self.seed_prng(0)
is_range = type(range_or_shape) is int
x = (range_or_shape if is_range else
self.rng().permutation(np.arange(
math.prod(range_or_shape), dtype=dtype)).reshape(range_or_shape))
shape = ((range_or_shape,) if is_range else range_or_shape)
x_ = np.copy(x)
rand = lambda key, x: random.permutation(key, x, axis, independent=independent)
perm = rand(key, x)
if shape[axis] >= 10:
self.assertFalse(np.all(perm == x)) # seems unlikely!
arr = np.arange(x) if is_range else x
def lsort(x):
if not math.prod(x.shape): return x
ind = np.lexsort(np.swapaxes(x, axis, -1).reshape((-1, x.shape[axis])))
return jnp.take(x, ind, axis)
if not independent:
self.assertArraysEqual(lsort(arr), lsort(perm), check_dtypes=not is_range)
if independent and (arr.shape[axis] > 4) and (arr.size // arr.shape[axis] > 4):
# Check for independent shuffling if there are >4 vectors of size >4.
# Chance of false positive is 1 in (5!)^4
with self.assertRaises(AssertionError):
self.assertArraysEqual(lsort(arr), lsort(perm), check_dtypes=not is_range)
self.assertArraysEqual(x_, x)
self.assertArraysEqual(perm, rand(key, np.array(x)))
self.assertArraysEqual(perm, jax.jit(rand, static_argnames=
'x' if is_range else None)(key, x))
def testPermutationErrors(self):
key = self.seed_prng(0)
with self.assertRaises(ValueError):
random.permutation(key, 10, axis=3)
with self.assertRaises(TypeError):
random.permutation(key, 10.)
with self.assertRaises(core.ConcretizationTypeError):
jax.jit(random.permutation)(key, 10)
@jtu.sample_product(
p=[0.1, 0.5, 0.9],
dtype=jtu.dtypes.floating,
)
def testBernoulli(self, p, dtype):
key = self.seed_prng(0)
p = np.array(p, dtype=dtype)
rand = lambda key, p: random.bernoulli(key, p, (10000,))
crand = jax.jit(rand)
uncompiled_samples = rand(key, p)
compiled_samples = crand(key, p)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckChiSquared(samples, scipy.stats.bernoulli(p).pmf)
@jtu.sample_product(
[dict(p=p, axis=axis)
for (p, axis) in [
([.25] * 4, -1),
([.1, .2, .3, .4], -1),
([[.5, .5], [.1, .9]], 1),
([[.5, .1], [.5, .9]], 0),
]
],
sample_shape=[(10000,), (5000, 2)],
dtype=jtu.dtypes.floating,
)
def testCategorical(self, p, axis, dtype, sample_shape):
key = self.seed_prng(0)
p = np.array(p, dtype=dtype)
logits = np.log(p) - 42 # test unnormalized
out_shape = tuple(np.delete(logits.shape, axis))
shape = sample_shape + out_shape
rand = partial(random.categorical, shape=shape, axis=axis)
crand = jax.jit(rand)
uncompiled_samples = rand(key, logits)
compiled_samples = crand(key, logits)
if axis < 0:
axis += len(logits.shape)
for samples in [uncompiled_samples, compiled_samples]:
assert samples.shape == shape
samples = jnp.reshape(samples, (10000,) + out_shape)
if len(p.shape[:-1]) > 0:
ps = np.transpose(p, (1, 0)) if axis == 0 else p
for cat_samples, cat_p in zip(samples.transpose(), ps):
pmf = lambda x: np.where(x < len(cat_p), cat_p[np.minimum(len(cat_p) - 1, x)], 0.0)
self._CheckChiSquared(cat_samples, pmf=pmf)
else:
pmf = lambda x: np.where(x < len(p), p[np.minimum(len(p) - 1, x)], 0.0)
self._CheckChiSquared(samples, pmf=pmf)
def testBernoulliShape(self):
key = self.seed_prng(0)
with jax.numpy_rank_promotion('allow'):
x = random.bernoulli(key, np.array([0.2, 0.3]), shape=(3, 2))
assert x.shape == (3, 2)
@jtu.sample_product(
a=[0.2, 5.],
b=[0.2, 5.],
dtype=[np.float64], # NOTE: KS test fails with float32
)
def testBeta(self, a, b, dtype):
if not config.x64_enabled:
raise SkipTest("skip test except on X64")
key = self.seed_prng(0)
rand = lambda key, a, b: random.beta(key, a, b, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key, a, b)
compiled_samples = crand(key, a, b)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.beta(a, b).cdf)
def testBetaSmallParameters(self, dtype=np.float32):
# Regression test for beta version of https://github.com/google/jax/issues/9896
key = self.seed_prng(0)
a, b = 0.0001, 0.0002
samples = random.beta(key, a, b, shape=(100,), dtype=dtype)
# With such small parameters, all samples should be exactly zero or one.
tol = 5E-2 if jtu.device_under_test() == "tpu" else 1E-3
zeros = samples[samples < 0.5]
self.assertAllClose(zeros, jnp.zeros_like(zeros), atol=tol)
ones = samples[samples >= 0.5]
self.assertAllClose(ones, jnp.ones_like(ones), atol=tol)
@jtu.sample_product(dtype=float_dtypes)
def testCauchy(self, dtype):
key = self.seed_prng(0)
rand = lambda key: random.cauchy(key, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key)
compiled_samples = crand(key)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.cauchy().cdf)
@jtu.sample_product(
alpha=[np.array([0.2, 1., 5.]),],
dtype=jtu.dtypes.floating,
)
@jtu.skip_on_devices("tpu") # TODO(mattjj): slow compilation times
def testDirichlet(self, alpha, dtype):
key = self.seed_prng(0)
rand = lambda key, alpha: random.dirichlet(key, alpha, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key, alpha)
compiled_samples = crand(key, alpha)
for samples in [uncompiled_samples, compiled_samples]:
self.assertAllClose(samples.sum(-1), np.ones(10000, dtype=dtype))
alpha_sum = sum(alpha)
for i, a in enumerate(alpha):
self._CheckKolmogorovSmirnovCDF(samples[..., i], scipy.stats.beta(a, alpha_sum - a).cdf)
def testDirichletSmallAlpha(self, dtype=np.float32):
# Regression test for https://github.com/google/jax/issues/9896
key = self.seed_prng(0)
alpha = 0.0001 * jnp.ones(3)
samples = random.dirichlet(key, alpha, shape=(100,), dtype=dtype)
# Check that results lie on the simplex.
self.assertAllClose(samples.sum(1), jnp.ones(samples.shape[0]),
check_dtypes=False, rtol=1E-5)
# Check that results contain 1 in one of the dimensions:
# this is highly likely to be true when alpha is small.
self.assertAllClose(samples.max(1), jnp.ones(samples.shape[0]),
check_dtypes=False, rtol=1E-4)
@jtu.sample_product(dtype=float_dtypes)
def testExponential(self, dtype):
key = self.seed_prng(0)
rand = lambda key: random.exponential(key, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key)
compiled_samples = crand(key)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.expon().cdf)
@jtu.sample_product(
a=[0.1, 1., 10.],
dtype=jtu.dtypes.floating,
)
def testGammaVsLogGamma(self, a, dtype):
key = self.seed_prng(0)
rand_gamma = lambda key, a: random.gamma(key, a, (10000,), dtype)
rand_loggamma = lambda key, a: random.loggamma(key, a, (10000,), dtype)
crand_loggamma = jax.jit(rand_loggamma)
self.assertAllClose(rand_gamma(key, a), jnp.exp(rand_loggamma(key, a)))
self.assertAllClose(rand_gamma(key, a), jnp.exp(crand_loggamma(key, a)))
@jtu.sample_product(
a=[0.1, 1., 10.],
dtype=jtu.dtypes.floating,
)
def testGamma(self, a, dtype):
key = self.seed_prng(0)
rand = lambda key, a: random.gamma(key, a, (10000,), dtype)
crand = jax.jit(rand)
uncompiled_samples = rand(key, a)
compiled_samples = crand(key, a)
for samples in [uncompiled_samples, compiled_samples]:
self._CheckKolmogorovSmirnovCDF(samples, scipy.stats.gamma(a).cdf)
def testGammaShape(self):
key = self.seed_prng(0)