# 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."""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import numpy as np
import tensorflow.compat.v2 as tf
from tensorflow_probability.python.bijectors import bijector


__all__ = [
    "Tanh",
]


class Tanh(bijector.Bijector):
  """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.Affine(shift=-1, scale=2.),
             tfb.Sigmoid(),
             tfb.Affine(scale=2.)])
  ```

  However, using the `Tanh` bijector directly is slightly faster and more
  numerically stable.
  """

  def __init__(self, validate_args=False, name="tanh"):
    super(Tanh, self).__init__(
        forward_min_event_ndims=0,
        validate_args=validate_args,
        name=name)

  def _forward(self, x):
    return tf.nn.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.nn.softplus(-2. * x))
