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.
  # ============================================================================
  """Distribution of a vectorized Exponential, with uncorrelated components."""
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import tensorflow.compat.v2 as tf
  from tensorflow_probability.python.distributions import vector_exponential_linear_operator as velo
  from tensorflow_probability.python.internal import dtype_util
  from tensorflow_probability.python.internal import tensor_util
  from tensorflow.python.util import deprecation  # pylint: disable=g-direct-tensorflow-import
  
  
  __all__ = [
      'VectorExponentialDiag',
  ]
  
  
  # Copied from distribution_util, where it is to be removed, and duplicated here
  # to support VectorExponentialDiag until the deprecation window is closed.
  def _make_diag_scale(loc=None,
                       scale_diag=None,
                       scale_identity_multiplier=None,
                       shape_hint=None,
                       validate_args=False,
                       assert_positive=False,
                       name=None,
                       dtype=None):
    """Creates a LinearOperator representing a diagonal matrix.
  
    Args:
      loc: Floating-point `Tensor`. This is used for inferring shape in the case
        where only `scale_identity_multiplier` is set.
      scale_diag: Floating-point `Tensor` representing the diagonal matrix.
        `scale_diag` has shape [N1, N2, ...  k], which represents a k x k diagonal
        matrix. When `None` no diagonal term is added to the LinearOperator.
      scale_identity_multiplier: floating point rank 0 `Tensor` representing a
        scaling done to the identity matrix. When `scale_identity_multiplier =
        scale_diag = scale_tril = None` then `scale += IdentityMatrix`. Otherwise
        no scaled-identity-matrix is added to `scale`.
      shape_hint: scalar integer `Tensor` representing a hint at the dimension of
        the identity matrix when only `scale_identity_multiplier` is set.
      validate_args: Python `bool` indicating whether arguments should be checked
        for correctness.
      assert_positive: Python `bool` indicating whether LinearOperator should be
        checked for being positive definite.
      name: Python `str` name given to ops managed by this object.
      dtype: TF `DType` to prefer when converting args to `Tensor`s. Else, we fall
        back to a compatible dtype across all of `loc`, `scale_diag`, and
        `scale_identity_multiplier`.
  
    Returns:
      `LinearOperator` representing a lower triangular matrix.
  
    Raises:
      ValueError:  If only `scale_identity_multiplier` is set and `loc` and
        `shape_hint` are both None.
    """
  
    with tf.name_scope(name or 'make_diag_scale'):
      if dtype is None:
        dtype = dtype_util.common_dtype(
            [loc, scale_diag, scale_identity_multiplier],
            dtype_hint=tf.float32)
      loc = tensor_util.convert_nonref_to_tensor(loc, name='loc', dtype=dtype)
      scale_diag = tensor_util.convert_nonref_to_tensor(
          scale_diag, name='scale_diag', dtype=dtype)
      scale_identity_multiplier = tensor_util.convert_nonref_to_tensor(
          scale_identity_multiplier,
          name='scale_identity_multiplier',
          dtype=dtype)
  
      if scale_diag is not None:
        if scale_identity_multiplier is not None:
          scale_diag = scale_diag + scale_identity_multiplier[..., tf.newaxis]
        return tf.linalg.LinearOperatorDiag(
            diag=scale_diag,
            is_non_singular=True,
            is_self_adjoint=True,
            is_positive_definite=assert_positive)
  
      if loc is None and shape_hint is None:
        raise ValueError('Cannot infer `event_shape` unless `loc` or '
                         '`shape_hint` is specified.')
  
      num_rows = shape_hint
      del shape_hint
      if num_rows is None:
        num_rows = tf.compat.dimension_value(loc.shape[-1])
        if num_rows is None:
          num_rows = tf.shape(loc)[-1]
  
      if scale_identity_multiplier is None:
        return tf.linalg.LinearOperatorIdentity(
            num_rows=num_rows,
            dtype=dtype,
            is_self_adjoint=True,
            is_positive_definite=True,
            assert_proper_shapes=validate_args)
  
      return tf.linalg.LinearOperatorScaledIdentity(
          num_rows=num_rows,
          multiplier=scale_identity_multiplier,
          is_non_singular=True,
          is_self_adjoint=True,
          is_positive_definite=assert_positive,
          assert_proper_shapes=validate_args)
  
  
  class VectorExponentialDiag(velo.VectorExponentialLinearOperator):
    """The vectorization of the Exponential distribution on `R^k`.
  
    The vector exponential distribution is defined over a subset of `R^k`, and
    parameterized by a (batch of) length-`k` `loc` vector and a (batch of) `k x k`
    `scale` matrix:  `covariance = scale @ scale.T`, where `@` denotes
    matrix-multiplication.
  
    #### Mathematical Details
  
    The probability density function (pdf) is defined over the image of the
    `scale` matrix + `loc`, applied to the positive half-space:
    `Supp = {loc + scale @ x : x in R^k, x_1 > 0, ..., x_k > 0}`.  On this set,
  
    ```none
    pdf(y; loc, scale) = exp(-||x||_1) / Z,  for y in Supp
    x = inv(scale) @ (y - loc),
    Z = |det(scale)|,
    ```
  
    where:
  
    * `loc` is a vector in `R^k`,
    * `scale` is a linear operator in `R^{k x k}`, `cov = scale @ scale.T`,
    * `Z` denotes the normalization constant, and,
    * `||x||_1` denotes the `l1` norm of `x`, `sum_i |x_i|`.
  
    The VectorExponential distribution is a member of the [location-scale
    family](https://en.wikipedia.org/wiki/Location-scale_family), i.e., it can be
    constructed as,
  
    ```none
    X = (X_1, ..., X_k), each X_i ~ Exponential(rate=1)
    Y = (Y_1, ...,Y_k) = scale @ X + loc
    ```
  
    #### About `VectorExponential` and `Vector` distributions in TensorFlow.
  
    The `VectorExponential` is a non-standard distribution that has useful
    properties.
  
    The marginals `Y_1, ..., Y_k` are *not* Exponential random variables, due to
    the fact that the sum of Exponential random variables is not Exponential.
  
    Instead, `Y` is a vector whose components are linear combinations of
    Exponential random variables.  Thus, `Y` lives in the vector space generated
    by `vectors` of Exponential distributions.  This allows the user to decide the
    mean and covariance (by setting `loc` and `scale`), while preserving some
    properties of the Exponential distribution.  In particular, the tails of `Y_i`
    will be (up to polynomial factors) exponentially decaying.
  
    To see this last statement, note that the pdf of `Y_i` is the convolution of
    the pdf of `k` independent Exponential random variables.  One can then show by
    induction that distributions with exponential (up to polynomial factors) tails
    are closed under convolution.
  
  
    #### Examples
  
    ```python
    tfd = tfp.distributions
  
    # Initialize a single 2-variate VectorExponential, supported on
    # {(x, y) in R^2 : x > 0, y > 0}.
  
    # The first component has pdf exp{-x}, the second 0.5 exp{-x / 2}
    vex = tfd.VectorExponentialDiag(scale_diag=[1., 2.])
  
    # Compute the pdf of an`R^2` observation; return a scalar.
    vex.prob([3., 4.]).eval()  # shape: []
  
    # Initialize a 2-batch of 3-variate Vector Exponential's.
    loc = [[1., 2, 3],
           [1., 0, 0]]              # shape: [2, 3]
    scale_diag = [[1., 2, 3],
                  [0.5, 1, 1.5]]     # shape: [2, 3]
  
    vex = tfd.VectorExponentialDiag(loc, scale_diag)
  
    # Compute the pdf of two `R^3` observations; return a length-2 vector.
    x = [[1.9, 2.2, 3.1],
         [10., 1.0, 9.0]]     # shape: [2, 3]
    vex.prob(x).eval()    # shape: [2]
    ```
  
    """
  
    @deprecation.deprecated(
        '2020-01-01',
        '`VectorExponentialDiag` is deprecated. If all you need is the diagonal '
        'scale, you can use '
        '`tfd.Independent(tfd.Exponential(1./scale_diag), 1)` instead. You '
        'can also directly use `VectorExponentialLinearOperator` with the '
        'appropriate `LinearOperator` instance.')
    def __init__(self,
                 loc=None,
                 scale_diag=None,
                 scale_identity_multiplier=None,
                 validate_args=False,
                 allow_nan_stats=True,
                 name='VectorExponentialDiag'):
      """Construct Vector Exponential distribution supported on a subset of `R^k`.
  
      The `batch_shape` is the broadcast shape between `loc` and `scale`
      arguments.
  
      The `event_shape` is given by last dimension of the matrix implied by
      `scale`. The last dimension of `loc` (if provided) must broadcast with this.
  
      Recall that `covariance = scale @ scale.T`.
  
      ```none
      scale = diag(scale_diag + scale_identity_multiplier * ones(k))
      ```
  
      where:
  
      * `scale_diag.shape = [k]`, and,
      * `scale_identity_multiplier.shape = []`.
  
      Additional leading dimensions (if any) will index batches.
  
      If both `scale_diag` and `scale_identity_multiplier` are `None`, then
      `scale` is the Identity matrix.
  
      Args:
        loc: Floating-point `Tensor`. If this is set to `None`, `loc` is
          implicitly `0`. When specified, may have shape `[B1, ..., Bb, k]` where
          `b >= 0` and `k` is the event size.
        scale_diag: Non-zero, floating-point `Tensor` representing a diagonal
          matrix added to `scale`. May have shape `[B1, ..., Bb, k]`, `b >= 0`,
          and characterizes `b`-batches of `k x k` diagonal matrices added to
          `scale`. When both `scale_identity_multiplier` and `scale_diag` are
          `None` then `scale` is the `Identity`.
        scale_identity_multiplier: Non-zero, floating-point `Tensor` representing
          a scaled-identity-matrix added to `scale`. May have shape
          `[B1, ..., Bb]`, `b >= 0`, and characterizes `b`-batches of scaled
          `k x k` identity matrices added to `scale`. When both
          `scale_identity_multiplier` and `scale_diag` are `None` then `scale` is
          the `Identity`.
        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.
  
      Raises:
        ValueError: if at most `scale_identity_multiplier` is specified.
      """
      parameters = dict(locals())
      with tf.name_scope(name) as name:
        with tf.name_scope('init'):
          # No need to validate_args while making diag_scale.  The returned
          # LinearOperatorDiag has an assert_non_singular method that is called by
          # the Bijector.
          scale = _make_diag_scale(
              loc=loc,
              scale_diag=scale_diag,
              scale_identity_multiplier=scale_identity_multiplier,
              validate_args=False,
              assert_positive=False)
      super(VectorExponentialDiag, self).__init__(
          loc=loc,
          scale=scale,
          validate_args=validate_args,
          allow_nan_stats=allow_nan_stats,
          name=name)
      self._parameters = parameters
  
    @classmethod
    def _params_event_ndims(cls):
      return dict(loc=1, scale_diag=1, scale_identity_multiplier=0)
  