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tanh.py
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tanh.py
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# Copyright 2018 The TensorFlow Probability 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
#
# 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.
# ============================================================================
"""Tanh bijector."""
import numpy as np
import tensorflow.compat.v2 as tf
from tensorflow_probability.python.bijectors import bijector
__all__ = [
'Tanh',
]
class Tanh(
bijector.CoordinatewiseBijectorMixin,
bijector.AutoCompositeTensorBijector):
"""Bijector that computes `Y = tanh(X)`, therefore `Y in (-1, 1)`.
This can be achieved by an affine transform of the Sigmoid bijector, i.e.,
it is equivalent to
```
tfb.Chain([tfb.Shift(shift=-1.),
tfb.Scale(scale=2.),
tfb.Sigmoid(),
tfb.Scale(scale=2.)])
```
However, using the `Tanh` bijector directly is slightly faster and more
numerically stable.
"""
def __init__(self, validate_args=False, name='tanh'):
parameters = dict(locals())
with tf.name_scope(name) as name:
super(Tanh, self).__init__(
forward_min_event_ndims=0,
validate_args=validate_args,
parameters=parameters,
name=name)
@classmethod
def _is_increasing(cls):
return True
@classmethod
def _parameter_properties(cls, dtype):
return dict()
def _forward(self, x):
return tf.math.tanh(x)
def _inverse(self, y):
return tf.atanh(y)
# We implicitly rely on _forward_log_det_jacobian rather than explicitly
# implement _inverse_log_det_jacobian since directly using
# `-tf.math.log1p(-tf.square(y))` has lower numerical precision.
def _forward_log_det_jacobian(self, x):
# This formula is mathematically equivalent to
# `tf.log1p(-tf.square(tf.tanh(x)))`, however this code is more numerically
# stable.
# Derivation:
# log(1 - tanh(x)^2)
# = log(sech(x)^2)
# = 2 * log(sech(x))
# = 2 * log(2e^-x / (e^-2x + 1))
# = 2 * (log(2) - x - log(e^-2x + 1))
# = 2 * (log(2) - x - softplus(-2x))
return 2. * (np.log(2.) - x - tf.math.softplus(-2. * x))