1# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
2#
3# Licensed under the Apache License, Version 2.0 (the "License");
4# you may not use this file except in compliance with the License.
5# You may obtain a copy of the License at
6#
7#     http://www.apache.org/licenses/LICENSE-2.0
8#
9# Unless required by applicable law or agreed to in writing, software
10# distributed under the License is distributed on an "AS IS" BASIS,
11# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12# See the License for the specific language governing permissions and
13# limitations under the License.
14# ==============================================================================
15"""The Exponential distribution class."""
16
17from __future__ import absolute_import
18from __future__ import division
19from __future__ import print_function
20
21import numpy as np
22
23from tensorflow.python.framework import dtypes
24from tensorflow.python.framework import ops
25from tensorflow.python.ops import array_ops
26from tensorflow.python.ops import math_ops
27from tensorflow.python.ops import nn
28from tensorflow.python.ops import random_ops
29from tensorflow.python.ops.distributions import gamma
30from tensorflow.python.util.tf_export import tf_export
31
32
33__all__ = [
34    "Exponential",
35    "ExponentialWithSoftplusRate",
36]
37
38
39@tf_export("distributions.Exponential")
40class Exponential(gamma.Gamma):
41  """Exponential distribution.
42
43  The Exponential distribution is parameterized by an event `rate` parameter.
44
45  #### Mathematical Details
46
47  The probability density function (pdf) is,
48
49  ```none
50  pdf(x; lambda, x > 0) = exp(-lambda x) / Z
51  Z = 1 / lambda
52  ```
53
54  where `rate = lambda` and `Z` is the normalizaing constant.
55
56  The Exponential distribution is a special case of the Gamma distribution,
57  i.e.,
58
59  ```python
60  Exponential(rate) = Gamma(concentration=1., rate)
61  ```
62
63  The Exponential distribution uses a `rate` parameter, or "inverse scale",
64  which can be intuited as,
65
66  ```none
67  X ~ Exponential(rate=1)
68  Y = X / rate
69  ```
70
71  """
72
73  def __init__(self,
74               rate,
75               validate_args=False,
76               allow_nan_stats=True,
77               name="Exponential"):
78    """Construct Exponential distribution with parameter `rate`.
79
80    Args:
81      rate: Floating point tensor, equivalent to `1 / mean`. Must contain only
82        positive values.
83      validate_args: Python `bool`, default `False`. When `True` distribution
84        parameters are checked for validity despite possibly degrading runtime
85        performance. When `False` invalid inputs may silently render incorrect
86        outputs.
87      allow_nan_stats: Python `bool`, default `True`. When `True`, statistics
88        (e.g., mean, mode, variance) use the value "`NaN`" to indicate the
89        result is undefined. When `False`, an exception is raised if one or
90        more of the statistic's batch members are undefined.
91      name: Python `str` name prefixed to Ops created by this class.
92    """
93    parameters = locals()
94    # Even though all statistics of are defined for valid inputs, this is not
95    # true in the parent class "Gamma."  Therefore, passing
96    # allow_nan_stats=True
97    # through to the parent class results in unnecessary asserts.
98    with ops.name_scope(name, values=[rate]):
99      self._rate = ops.convert_to_tensor(rate, name="rate")
100    super(Exponential, self).__init__(
101        concentration=array_ops.ones([], dtype=self._rate.dtype),
102        rate=self._rate,
103        allow_nan_stats=allow_nan_stats,
104        validate_args=validate_args,
105        name=name)
106    # While the Gamma distribution is not reparameterizable, the exponential
107    # distribution is.
108    self._reparameterization_type = True
109    self._parameters = parameters
110    self._graph_parents += [self._rate]
111
112  @staticmethod
113  def _param_shapes(sample_shape):
114    return {"rate": ops.convert_to_tensor(sample_shape, dtype=dtypes.int32)}
115
116  @property
117  def rate(self):
118    return self._rate
119
120  def _sample_n(self, n, seed=None):
121    shape = array_ops.concat([[n], array_ops.shape(self._rate)], 0)
122    # Uniform variates must be sampled from the open-interval `(0, 1)` rather
123    # than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_dtype).tiny`
124    # because it is the smallest, positive, "normal" number. A "normal" number
125    # is such that the mantissa has an implicit leading 1. Normal, positive
126    # numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In
127    # this case, a subnormal number (i.e., np.nextafter) can cause us to sample
128    # 0.
129    sampled = random_ops.random_uniform(
130        shape,
131        minval=np.finfo(self.dtype.as_numpy_dtype).tiny,
132        maxval=1.,
133        seed=seed,
134        dtype=self.dtype)
135    return -math_ops.log(sampled) / self._rate
136
137
138class ExponentialWithSoftplusRate(Exponential):
139  """Exponential with softplus transform on `rate`."""
140
141  def __init__(self,
142               rate,
143               validate_args=False,
144               allow_nan_stats=True,
145               name="ExponentialWithSoftplusRate"):
146    parameters = locals()
147    with ops.name_scope(name, values=[rate]):
148      super(ExponentialWithSoftplusRate, self).__init__(
149          rate=nn.softplus(rate, name="softplus_rate"),
150          validate_args=validate_args,
151          allow_nan_stats=allow_nan_stats,
152          name=name)
153    self._parameters = parameters
154