text: # 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.
  # ============================================================================
  """Relaxed OneHotCategorical distribution classes."""
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  # Dependency imports
  import numpy as np
  import tensorflow.compat.v2 as tf
  from tensorflow_probability.python.bijectors import chain as chain_bijector
  from tensorflow_probability.python.bijectors import exp as exp_bijector
  from tensorflow_probability.python.bijectors import softmax_centered as softmax_centered_bijector
  from tensorflow_probability.python.bijectors import softplus as softplus_bijector
  from tensorflow_probability.python.distributions import distribution
  from tensorflow_probability.python.distributions import transformed_distribution
  from tensorflow_probability.python.internal import assert_util
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import parameter_properties
  from tensorflow_probability.python.internal import prefer_static as ps
  from tensorflow_probability.python.internal import reparameterization
  from tensorflow_probability.python.internal import samplers
  from tensorflow_probability.python.internal import tensor_util
  from tensorflow_probability.python.internal import tensorshape_util
  from tensorflow.python.util import deprecation  # pylint: disable=g-direct-tensorflow-import
  
  
  class ExpRelaxedOneHotCategorical(distribution.AutoCompositeTensorDistribution):
    """ExpRelaxedOneHotCategorical distribution with temperature and logits.
  
    An ExpRelaxedOneHotCategorical distribution is a log-transformed
    RelaxedOneHotCategorical distribution. The RelaxedOneHotCategorical is a
    distribution over random probability vectors, vectors of positive real
    values that sum to one, which continuously approximates a OneHotCategorical.
    The degree of approximation is controlled by a temperature: as the temperature
    goes to 0 the RelaxedOneHotCategorical becomes discrete with a distribution
    described by the logits, as the temperature goes to infinity the
    RelaxedOneHotCategorical becomes the constant distribution that is identically
    the constant vector of (1/event_size, ..., 1/event_size).
  
    Because computing log-probabilities of the RelaxedOneHotCategorical can
    suffer from underflow issues, this class is one solution for loss
    functions that depend on log-probabilities, such as the KL Divergence found
    in the variational autoencoder loss. The KL divergence between two
    distributions is invariant under invertible transformations, so evaluating
    KL divergences of ExpRelaxedOneHotCategorical samples, which are always
    followed by a `tf.exp` op, is equivalent to evaluating KL divergences of
    RelaxedOneHotCategorical samples. See the appendix of Maddison et al., 2016
    for more mathematical details, where this distribution is called the
    ExpConcrete.
  
    #### Examples
  
    Creates a continuous distribution, whose exp approximates a 3-class one-hot
    categorical distribution. The 2nd class is the most likely to be the
    largest component in samples drawn from this distribution. If those samples
    are followed by a `tf.exp` op, then they are distributed as a relaxed onehot
    categorical.
  
    ```python
    temperature = 0.5
    p = [0.1, 0.5, 0.4]
    dist = ExpRelaxedOneHotCategorical(temperature, probs=p)
    samples = dist.sample()
    exp_samples = tf.exp(samples)
    # exp_samples has the same distribution as samples from
    # RelaxedOneHotCategorical(temperature, probs=p)
    ```
  
    Creates a continuous distribution, whose exp approximates a 3-class one-hot
    categorical distribution. The 2nd class is the most likely to be the
    largest component in samples drawn from this distribution.
  
    ```python
    temperature = 0.5
    logits = [-2, 2, 0]
    dist = ExpRelaxedOneHotCategorical(temperature, logits=logits)
    samples = dist.sample()
    exp_samples = tf.exp(samples)
    # exp_samples has the same distribution as samples from
    # RelaxedOneHotCategorical(temperature, probs=p)
    ```
  
    Creates a continuous distribution, whose exp approximates a 3-class one-hot
    categorical distribution. Because the temperature is very low, samples from
    this distribution are almost discrete, with one component almost 0 and the
    others very negative. The 2nd class is the most likely to be the largest
    component in samples drawn from this distribution.
  
    ```python
    temperature = 1e-5
    logits = [-2, 2, 0]
    dist = ExpRelaxedOneHotCategorical(temperature, logits=logits)
    samples = dist.sample()
    exp_samples = tf.exp(samples)
    # exp_samples has the same distribution as samples from
    # RelaxedOneHotCategorical(temperature, probs=p)
    ```
  
    Creates a continuous distribution, whose exp approximates a 3-class one-hot
    categorical distribution. Because the temperature is very high, samples from
    this distribution are usually close to the (-log(3), -log(3), -log(3)) vector.
    The 2nd class is still the most likely to be the largest component
    in samples drawn from this distribution.
  
    ```python
    temperature = 10
    logits = [-2, 2, 0]
    dist = ExpRelaxedOneHotCategorical(temperature, logits=logits)
    samples = dist.sample()
    exp_samples = tf.exp(samples)
    # exp_samples has the same distribution as samples from
    # RelaxedOneHotCategorical(temperature, probs=p)
    ```
  
    Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution:
    A Continuous Relaxation of Discrete Random Variables. 2016.
    """
  
    def __init__(
        self,
        temperature,
        logits=None,
        probs=None,
        validate_args=False,
        allow_nan_stats=True,
        name='ExpRelaxedOneHotCategorical'):
      """Initialize ExpRelaxedOneHotCategorical using class log-probabilities.
  
      Args:
        temperature: A `Tensor`, representing the temperature of one or more
          distributions. The temperature values must be positive, and the shape
          must broadcast against `(logits or probs)[..., 0]`.
        logits: An N-D `Tensor`, `N >= 1`, representing the log probabilities
          of one or many distributions. The first `N - 1` dimensions index into a
          batch of independent distributions and the last dimension represents a
          vector of logits for each class. Only one of `logits` or `probs` should
          be passed in.
        probs: An N-D `Tensor`, `N >= 1`, representing the probabilities
          of one or many distributions. The first `N - 1` dimensions index into a
          batch of independent distributions and the last dimension represents a
          vector of probabilities for each class. Only one of `logits` or `probs`
          should be passed in.
        validate_args: Python `bool`, default `False`. When `True` distribution
          parameters are checked for validity despite possibly degrading runtime
          performance. When `False` invalid inputs may silently render incorrect
          outputs.
        allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
          (e.g., mean, mode, variance) use the value "`NaN`" to indicate the
          result is undefined. When `False`, an exception is raised if one or
          more of the statistic's batch members are undefined.
        name: Python `str` name prefixed to Ops created by this class.
      """
      parameters = dict(locals())
      with tf.name_scope(name) as name:
        dtype = dtype_util.common_dtype([logits, probs, temperature], tf.float32)
        self._temperature = tensor_util.convert_nonref_to_tensor(
            temperature, dtype_hint=dtype, name='temperature')
        self._logits = tensor_util.convert_nonref_to_tensor(
            logits, dtype_hint=dtype, name='logits')
        self._probs = tensor_util.convert_nonref_to_tensor(
            probs, dtype_hint=dtype, name='probs')
        if (self._probs is None) == (self._logits is None):
          raise ValueError('Must pass `probs` or `logits`, but not both.')
  
        super(ExpRelaxedOneHotCategorical, self).__init__(
            dtype=dtype,
            reparameterization_type=reparameterization.FULLY_REPARAMETERIZED,
            validate_args=validate_args,
            allow_nan_stats=allow_nan_stats,
            parameters=parameters,
            name=name)
  
    @classmethod
    def _parameter_properties(cls, dtype, num_classes=None):
      # pylint: disable=g-long-lambda
      return dict(
          temperature=parameter_properties.ParameterProperties(
              shape_fn=lambda sample_shape: sample_shape[:-1],
              default_constraining_bijector_fn=(
                  lambda: softplus_bijector.Softplus(low=dtype_util.eps(dtype)))),
          logits=parameter_properties.ParameterProperties(event_ndims=1),
          probs=parameter_properties.ParameterProperties(
              event_ndims=1,
              default_constraining_bijector_fn=softmax_centered_bijector
              .SoftmaxCentered,
              is_preferred=False))
      # pylint: enable=g-long-lambda
  
    @property
    @deprecation.deprecated(
        '2019-10-01', 'The `event_size` property is deprecated.  Use '
        '`tf.shape(self.probs if self.logits is None else self.logits)[-1]` '
        'instead.')
    def event_size(self):
      """Scalar `int32` tensor: the number of classes."""
      return self._event_size()
  
    def _event_size(self, logits=None):
      param = logits
      if param is None:
        param = self._logits if self._logits is not None else self._probs
      if param.shape is not None:
        event_size = tf.compat.dimension_value(param.shape[-1])
        if event_size is not None:
          return event_size
      return tf.shape(param)[-1]
  
    @property
    def temperature(self):
      """Batchwise temperature tensor of a RelaxedCategorical."""
      return self._temperature
  
    @property
    def logits(self):
      """Input argument `logits`."""
      return self._logits
  
    @property
    def probs(self):
      """Input argument `probs`."""
      return self._probs
  
    def _event_shape_tensor(self, logits=None):
      param = logits
      if param is None:
        param = self._logits if self._logits is not None else self._probs
      return ps.shape(param)[-1:]
  
    def _event_shape(self):
      param = self._logits if self._logits is not None else self._probs
      return tensorshape_util.with_rank(param.shape[-1:], rank=1)
  
    def _sample_n(self, n, seed=None):
      temperature = tf.convert_to_tensor(self.temperature)
      logits = self._logits_parameter_no_checks()
  
      # Uniform variates must be sampled from the open-interval `(0, 1)` rather
      # than `[0, 1)`. To do so, we use
      # `np.finfo(dtype_util.as_numpy_dtype(self.dtype)).tiny` because it is the
      # smallest, positive, 'normal' number. A 'normal' number is such that the
      # mantissa has an implicit leading 1. Normal, positive numbers x, y have the
      # reasonable property that, `x + y >= max(x, y)`. In this case, a subnormal
      # number (i.e., np.nextafter) can cause us to sample 0.
      uniform_shape = ps.concat(
          [[n],
           self._batch_shape_tensor(temperature=temperature, logits=logits),
           self._event_shape_tensor(logits=logits)], 0)
      uniform = samplers.uniform(
          shape=uniform_shape,
          minval=np.finfo(dtype_util.as_numpy_dtype(self.dtype)).tiny,
          maxval=1.,
          dtype=self.dtype,
          seed=seed)
      gumbel = -tf.math.log(-tf.math.log(uniform))
      noisy_logits = (gumbel + logits) / temperature[..., tf.newaxis]
      return tf.math.log_softmax(noisy_logits)
  
    def _log_prob(self, x):
      temperature = tf.convert_to_tensor(self.temperature)
      logits = self._logits_parameter_no_checks()
  
      # broadcast logits or x if need be.
      if (not tensorshape_util.is_fully_defined(x.shape) or
          not tensorshape_util.is_fully_defined(logits.shape) or
          x.shape != logits.shape):
        logits = tf.ones_like(x, dtype=logits.dtype) * logits
        x = tf.ones_like(logits, dtype=x.dtype) * x
      # compute the normalization constant
      k = tf.cast(self._event_size(logits), x.dtype)
      log_norm_const = (
          tf.math.lgamma(k) + (k - 1.) * tf.math.log(temperature))
      # compute the unnormalized density
      log_softmax = tf.math.log_softmax(logits - x * temperature[..., tf.newaxis])
      log_unnorm_prob = tf.reduce_sum(log_softmax, axis=[-1], keepdims=False)
      # combine unnormalized density with normalization constant
      return log_norm_const + log_unnorm_prob
  
    def logits_parameter(self, name=None):
      """Logits vec computed from non-`None` input arg (`probs` or `logits`)."""
      with self._name_and_control_scope(name or 'logits_parameter'):
        return self._logits_parameter_no_checks()
  
    def _logits_parameter_no_checks(self):
      if self._logits is None:
        return tf.math.log(self._probs)
      return tensor_util.identity_as_tensor(self._logits)
  
    def probs_parameter(self, name=None):
      """Probs vec computed from non-`None` input arg (`probs` or `logits`)."""
      with self._name_and_control_scope(name or 'probs_parameter'):
        return self._probs_parameter_no_checks()
  
    def _probs_parameter_no_checks(self):
      if self._logits is None:
        return tensor_util.identity_as_tensor(self._probs)
      return tf.math.softmax(self._logits)
  
    def _sample_control_dependencies(self, x):
      assertions = []
      if not self.validate_args:
        return assertions
      assertions.append(assert_util.assert_non_positive(
          x,
          message=('Samples must be less than or equal to `0` for '
                   '`ExpRelaxedOneHotCategorical` or `1` for '
                   '`RelaxedOneHotCategorical`.')))
      assertions.append(assert_util.assert_near(
          tf.zeros([], dtype=self.dtype), tf.reduce_logsumexp(x, axis=[-1]),
          message=('Final dimension of samples must sum to `0` for ''.'
                   '`ExpRelaxedOneHotCategorical` or `1` '
                   'for `RelaxedOneHotCategorical`.')))
      return assertions
  
    def _parameter_control_dependencies(self, is_init):
      assertions = []
  
      logits = self._logits
      probs = self._probs
      param, name = (probs, 'probs') if logits is None else (logits, 'logits')
  
      # In init, we can always build shape and dtype checks because
      # we assume shape doesn't change for Variable backed args.
      if is_init:
        if not dtype_util.is_floating(param.dtype):
          raise TypeError('Argument `{}` must having floating type.'.format(name))
  
        msg = 'Argument `{}` must have rank at least 1.'.format(name)
        shape_static = tensorshape_util.dims(param.shape)
        if shape_static is not None:
          if len(shape_static) < 1:
            raise ValueError(msg)
        elif self.validate_args:
          param = tf.convert_to_tensor(param)
          assertions.append(
              assert_util.assert_rank_at_least(param, 1, message=msg))
  
        msg1 = 'Argument `{}` must have final dimension >= 1.'.format(name)
        msg2 = 'Argument `{}` must have final dimension <= {}.'.format(
            name, dtype_util.max(tf.int32))
        event_size = shape_static[-1] if shape_static is not None else None
        if event_size is not None:
          if event_size < 1:
            raise ValueError(msg1)
          if event_size > dtype_util.max(tf.int32):
            raise ValueError(msg2)
        elif self.validate_args:
          param = tf.convert_to_tensor(param)
          assertions.append(assert_util.assert_greater_equal(
              tf.shape(param)[-1:], 1, message=msg1))
          # NOTE: For now, we leave out a runtime assertion that
          # `tf.shape(param)[-1] <= tf.int32.max`.  An earlier `tf.shape` call
          # will fail before we get to this point.
  
      if not self.validate_args:
        assert not assertions  # Should never happen.
        return []
  
      if is_init != tensor_util.is_ref(self.temperature):
        assertions.append(assert_util.assert_positive(self.temperature))
  
      if probs is not None:
        probs = param  # reuse tensor conversion from above
        if is_init != tensor_util.is_ref(probs):
          probs = tf.convert_to_tensor(probs)
          one = tf.ones([], dtype=probs.dtype)
          assertions.extend([
              assert_util.assert_non_negative(probs),
              assert_util.assert_less_equal(probs, one),
              assert_util.assert_near(
                  tf.reduce_sum(probs, axis=-1), one,
                  message='Argument `probs` must sum to 1.'),
          ])
  
      return assertions
  
    def _default_event_space_bijector(self):
      # TODO(b/145620027) Finalize choice of bijector.
      return chain_bijector.Chain([
          exp_bijector.Log(validate_args=self.validate_args),
          softmax_centered_bijector.SoftmaxCentered(
              validate_args=self.validate_args),
      ], validate_args=self.validate_args)
  
  
  class RelaxedOneHotCategorical(
      transformed_distribution.TransformedDistribution,
      distribution.AutoCompositeTensorDistribution):
    """RelaxedOneHotCategorical distribution with temperature and logits.
  
    The RelaxedOneHotCategorical is a distribution over random probability
    vectors, vectors of positive real values that sum to one, which continuously
    approximates a OneHotCategorical. The degree of approximation is controlled by
    a temperature: as the temperature goes to 0 the RelaxedOneHotCategorical
    becomes discrete with a distribution described by the `logits` or `probs`
    parameters, as the temperature goes to infinity the RelaxedOneHotCategorical
    becomes the constant distribution that is identically the constant vector of
    (1/event_size, ..., 1/event_size).
  
    The RelaxedOneHotCategorical distribution was concurrently introduced as the
    Gumbel-Softmax (Jang et al., 2016) and Concrete (Maddison et al., 2016)
    distributions for use as a reparameterized continuous approximation to the
    `Categorical` one-hot distribution. If you use this distribution, please cite
    both papers.
  
    #### Examples
  
    Creates a continuous distribution, which approximates a 3-class one-hot
    categorical distribution. The 2nd class is the most likely to be the
    largest component in samples drawn from this distribution.
  
    ```python
    temperature = 0.5
    p = [0.1, 0.5, 0.4]
    dist = RelaxedOneHotCategorical(temperature, probs=p)
    ```
  
    Creates a continuous distribution, which approximates a 3-class one-hot
    categorical distribution. The 2nd class is the most likely to be the
    largest component in samples drawn from this distribution.
  
    ```python
    temperature = 0.5
    logits = [-2, 2, 0]
    dist = RelaxedOneHotCategorical(temperature, logits=logits)
    ```
  
    Creates a continuous distribution, which approximates a 3-class one-hot
    categorical distribution. Because the temperature is very low, samples from
    this distribution are almost discrete, with one component almost 1 and the
    others nearly 0. The 2nd class is the most likely to be the largest component
    in samples drawn from this distribution.
  
    ```python
    temperature = 1e-5
    logits = [-2, 2, 0]
    dist = RelaxedOneHotCategorical(temperature, logits=logits)
    ```
  
    Creates a continuous distribution, which approximates a 3-class one-hot
    categorical distribution. Because the temperature is very high, samples from
    this distribution are usually close to the (1/3, 1/3, 1/3) vector. The 2nd
    class is still the most likely to be the largest component
    in samples drawn from this distribution.
  
    ```python
    temperature = 10
    logits = [-2, 2, 0]
    dist = RelaxedOneHotCategorical(temperature, logits=logits)
    ```
  
    Eric Jang, Shixiang Gu, and Ben Poole. Categorical Reparameterization with
    Gumbel-Softmax. 2016.
  
    Chris J. Maddison, Andriy Mnih, and Yee Whye Teh. The Concrete Distribution:
    A Continuous Relaxation of Discrete Random Variables. 2016.
    """
  
    def __init__(
        self,
        temperature,
        logits=None,
        probs=None,
        validate_args=False,
        allow_nan_stats=True,
        name='RelaxedOneHotCategorical'):
      """Initialize RelaxedOneHotCategorical using class log-probabilities.
  
      Args:
        temperature: An 0-D `Tensor`, representing the temperature
          of a set of RelaxedOneHotCategorical distributions. The temperature
          should be positive.
        logits: An N-D `Tensor`, `N >= 1`, representing the log probabilities
          of a set of RelaxedOneHotCategorical distributions. The first
          `N - 1` dimensions index into a batch of independent distributions and
          the last dimension represents a vector of logits for each class. Only
          one of `logits` or `probs` should be passed in.
        probs: An N-D `Tensor`, `N >= 1`, representing the probabilities
          of a set of RelaxedOneHotCategorical distributions. The first `N - 1`
          dimensions index into a batch of independent distributions and the last
          dimension represents a vector of probabilities for each class. Only one
          of `logits` or `probs` should be passed in.
        validate_args: Unused in this distribution.
        allow_nan_stats: Python `bool`, default `True`. If `False`, raise an
          exception if a statistic (e.g. mean/mode/etc...) is undefined for any
          batch member. If `True`, batch members with valid parameters leading to
          undefined statistics will return NaN for this statistic.
        name: A name for this distribution (optional).
      """
      parameters = dict(locals())
      dist = ExpRelaxedOneHotCategorical(temperature,
                                         logits=logits,
                                         probs=probs,
                                         validate_args=validate_args,
                                         allow_nan_stats=allow_nan_stats)
  
      super(RelaxedOneHotCategorical, self).__init__(dist,
                                                     exp_bijector.Exp(),
                                                     validate_args=validate_args,
                                                     parameters=parameters,
                                                     name=name)
  
    @classmethod
    def _parameter_properties(cls, dtype, num_classes=None):
      # pylint: disable=g-long-lambda
      return dict(
          temperature=parameter_properties.ParameterProperties(
              shape_fn=lambda sample_shape: sample_shape[:-1],
              default_constraining_bijector_fn=(
                  lambda: softplus_bijector.Softplus(low=dtype_util.eps(dtype)))),
          logits=parameter_properties.ParameterProperties(event_ndims=1),
          probs=parameter_properties.ParameterProperties(
              event_ndims=1,
              default_constraining_bijector_fn=softmax_centered_bijector
              .SoftmaxCentered,
              is_preferred=False))
      # pylint: enable=g-long-lambda
  
    @property
    def temperature(self):
      """Batchwise temperature tensor of a RelaxedCategorical."""
      return self.distribution.temperature
  
    @property
    @deprecation.deprecated(
        '2019-10-01', 'The `event_size` property is deprecated.  Use '
        '`tf.shape(self.probs if self.logits is None else self.logits)[-1]` '
        'instead.')
    def event_size(self):
      """Scalar `int32` tensor: the number of classes."""
      return self.distribution.event_size
  
    @property
    def probs(self):
      """Input argument `probs`."""
      return self.distribution.probs
  
    @property
    def logits(self):
      """Input argument `logits`."""
      return self.distribution.logits
  
    experimental_is_sharded = False
  
    def logits_parameter(self, name=None):
      """Logits vec computed from non-`None` input arg (`probs` or `logits`)."""
      return self.distribution.logits_parameter(name)
  
    def probs_parameter(self, name=None):
      """Probs vec computed from non-`None` input arg (`probs` or `logits`)."""
      return self.distribution.probs_parameter(name)
  
    def _default_event_space_bijector(self):
      return softmax_centered_bijector.SoftmaxCentered(
          validate_args=self.validate_args)
  