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# Copyright 2016 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.
# ==============================================================================
"""Bijector unit-test utilities."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.python.framework import ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops.distributions import uniform as uniform_lib
def assert_finite(array):
if not np.isfinite(array).all():
raise AssertionError("array was not all finite. %s" % array[:15])
def assert_strictly_increasing(array):
np.testing.assert_array_less(0., np.diff(array))
def assert_strictly_decreasing(array):
np.testing.assert_array_less(np.diff(array), 0.)
def assert_strictly_monotonic(array):
if array[0] < array[-1]:
assert_strictly_increasing(array)
else:
assert_strictly_decreasing(array)
def assert_scalar_congruency(bijector,
lower_x,
upper_x,
n=int(10e3),
rtol=0.01,
sess=None):
"""Assert `bijector`'s forward/inverse/inverse_log_det_jacobian are congruent.
We draw samples `X ~ U(lower_x, upper_x)`, then feed these through the
`bijector` in order to check that:
1. the forward is strictly monotonic.
2. the forward/inverse methods are inverses of each other.
3. the jacobian is the correct change of measure.
This can only be used for a Bijector mapping open subsets of the real line
to themselves. This is due to the fact that this test compares the `prob`
before/after transformation with the Lebesgue measure on the line.
Args:
bijector: Instance of Bijector
lower_x: Python scalar.
upper_x: Python scalar. Must have `lower_x < upper_x`, and both must be in
the domain of the `bijector`. The `bijector` should probably not produce
huge variation in values in the interval `(lower_x, upper_x)`, or else
the variance based check of the Jacobian will require small `rtol` or
huge `n`.
n: Number of samples to draw for the checks.
rtol: Positive number. Used for the Jacobian check.
sess: `tf.Session`. Defaults to the default session.
Raises:
AssertionError: If tests fail.
"""
# Checks and defaults.
assert bijector.event_ndims.eval() == 0
if sess is None:
sess = ops.get_default_session()
# Should be monotonic over this interval
ten_x_pts = np.linspace(lower_x, upper_x, num=10).astype(np.float32)
if bijector.dtype is not None:
ten_x_pts = ten_x_pts.astype(bijector.dtype.as_numpy_dtype)
forward_on_10_pts = bijector.forward(ten_x_pts)
# Set the lower/upper limits in the range of the bijector.
lower_y, upper_y = sess.run(
[bijector.forward(lower_x), bijector.forward(upper_x)])
if upper_y < lower_y: # If bijector.forward is a decreasing function.
lower_y, upper_y = upper_y, lower_y
# Uniform samples from the domain, range.
uniform_x_samps = uniform_lib.Uniform(
low=lower_x, high=upper_x).sample(n, seed=0)
uniform_y_samps = uniform_lib.Uniform(
low=lower_y, high=upper_y).sample(n, seed=1)
# These compositions should be the identity.
inverse_forward_x = bijector.inverse(bijector.forward(uniform_x_samps))
forward_inverse_y = bijector.forward(bijector.inverse(uniform_y_samps))
# For a < b, and transformation y = y(x),
# (b - a) = \int_a^b dx = \int_{y(a)}^{y(b)} |dx/dy| dy
# "change_measure_dy_dx" below is a Monte Carlo approximation to the right
# hand side, which should then be close to the left, which is (b - a).
dy_dx = math_ops.exp(bijector.inverse_log_det_jacobian(uniform_y_samps))
# E[|dx/dy|] under Uniform[lower_y, upper_y]
# = \int_{y(a)}^{y(b)} |dx/dy| dP(u), where dP(u) is the uniform measure
expectation_of_dy_dx_under_uniform = math_ops.reduce_mean(dy_dx)
# dy = dP(u) * (upper_y - lower_y)
change_measure_dy_dx = (
(upper_y - lower_y) * expectation_of_dy_dx_under_uniform)
# We'll also check that dy_dx = 1 / dx_dy.
dx_dy = math_ops.exp(
bijector.forward_log_det_jacobian(bijector.inverse(uniform_y_samps)))
[
forward_on_10_pts_v,
dy_dx_v,
dx_dy_v,
change_measure_dy_dx_v,
uniform_x_samps_v,
uniform_y_samps_v,
inverse_forward_x_v,
forward_inverse_y_v,
] = sess.run([
forward_on_10_pts,
dy_dx,
dx_dy,
change_measure_dy_dx,
uniform_x_samps,
uniform_y_samps,
inverse_forward_x,
forward_inverse_y,
])
assert_strictly_monotonic(forward_on_10_pts_v)
# Composition of forward/inverse should be the identity.
np.testing.assert_allclose(
inverse_forward_x_v, uniform_x_samps_v, atol=1e-5, rtol=1e-3)
np.testing.assert_allclose(
forward_inverse_y_v, uniform_y_samps_v, atol=1e-5, rtol=1e-3)
# Change of measure should be correct.
np.testing.assert_allclose(
upper_x - lower_x, change_measure_dy_dx_v, atol=0, rtol=rtol)
# Inverse Jacobian should be equivalent to the reciprocal of the forward
# Jacobian.
np.testing.assert_allclose(
dy_dx_v, np.divide(1., dx_dy_v), atol=1e-5, rtol=1e-3)
def assert_bijective_and_finite(bijector, x, y, atol=0, rtol=1e-5, sess=None):
"""Assert that forward/inverse (along with jacobians) are inverses and finite.
It is recommended to use x and y values that are very very close to the edge
of the Bijector's domain.
Args:
bijector: A Bijector instance.
x: np.array of values in the domain of bijector.forward.
y: np.array of values in the domain of bijector.inverse.
atol: Absolute tolerance.
rtol: Relative tolerance.
sess: TensorFlow session. Defaults to the default session.
Raises:
AssertionError: If tests fail.
"""
sess = sess or ops.get_default_session()
# These are the incoming points, but people often create a crazy range of
# values for which these end up being bad, especially in 16bit.
assert_finite(x)
assert_finite(y)
f_x = bijector.forward(x)
g_y = bijector.inverse(y)
[
x_from_x,
y_from_y,
ildj_f_x,
fldj_x,
ildj_y,
fldj_g_y,
f_x_v,
g_y_v,
] = sess.run([
bijector.inverse(f_x),
bijector.forward(g_y),
bijector.inverse_log_det_jacobian(f_x),
bijector.forward_log_det_jacobian(x),
bijector.inverse_log_det_jacobian(y),
bijector.forward_log_det_jacobian(g_y),
f_x,
g_y,
])
assert_finite(x_from_x)
assert_finite(y_from_y)
assert_finite(ildj_f_x)
assert_finite(fldj_x)
assert_finite(ildj_y)
assert_finite(fldj_g_y)
assert_finite(f_x_v)
assert_finite(g_y_v)
np.testing.assert_allclose(x_from_x, x, atol=atol, rtol=rtol)
np.testing.assert_allclose(y_from_y, y, atol=atol, rtol=rtol)
np.testing.assert_allclose(-ildj_f_x, fldj_x, atol=atol, rtol=rtol)
np.testing.assert_allclose(-ildj_y, fldj_g_y, atol=atol, rtol=rtol)
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