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 import deprecation 31from tensorflow.python.util.tf_export import tf_export 32 33 34__all__ = [ 35 "Exponential", 36 "ExponentialWithSoftplusRate", 37] 38 39 40@tf_export(v1=["distributions.Exponential"]) 41class Exponential(gamma.Gamma): 42 """Exponential distribution. 43 44 The Exponential distribution is parameterized by an event `rate` parameter. 45 46 #### Mathematical Details 47 48 The probability density function (pdf) is, 49 50 ```none 51 pdf(x; lambda, x > 0) = exp(-lambda x) / Z 52 Z = 1 / lambda 53 ``` 54 55 where `rate = lambda` and `Z` is the normalizaing constant. 56 57 The Exponential distribution is a special case of the Gamma distribution, 58 i.e., 59 60 ```python 61 Exponential(rate) = Gamma(concentration=1., rate) 62 ``` 63 64 The Exponential distribution uses a `rate` parameter, or "inverse scale", 65 which can be intuited as, 66 67 ```none 68 X ~ Exponential(rate=1) 69 Y = X / rate 70 ``` 71 72 """ 73 74 @deprecation.deprecated( 75 "2019-01-01", 76 "The TensorFlow Distributions library has moved to " 77 "TensorFlow Probability " 78 "(https://github.com/tensorflow/probability). You " 79 "should update all references to use `tfp.distributions` " 80 "instead of `tf.distributions`.", 81 warn_once=True) 82 def __init__(self, 83 rate, 84 validate_args=False, 85 allow_nan_stats=True, 86 name="Exponential"): 87 """Construct Exponential distribution with parameter `rate`. 88 89 Args: 90 rate: Floating point tensor, equivalent to `1 / mean`. Must contain only 91 positive values. 92 validate_args: Python `bool`, default `False`. When `True` distribution 93 parameters are checked for validity despite possibly degrading runtime 94 performance. When `False` invalid inputs may silently render incorrect 95 outputs. 96 allow_nan_stats: Python `bool`, default `True`. When `True`, statistics 97 (e.g., mean, mode, variance) use the value "`NaN`" to indicate the 98 result is undefined. When `False`, an exception is raised if one or 99 more of the statistic's batch members are undefined. 100 name: Python `str` name prefixed to Ops created by this class. 101 """ 102 parameters = dict(locals()) 103 # Even though all statistics of are defined for valid inputs, this is not 104 # true in the parent class "Gamma." Therefore, passing 105 # allow_nan_stats=True 106 # through to the parent class results in unnecessary asserts. 107 with ops.name_scope(name, values=[rate]) as name: 108 self._rate = ops.convert_to_tensor(rate, name="rate") 109 super(Exponential, self).__init__( 110 concentration=array_ops.ones([], dtype=self._rate.dtype), 111 rate=self._rate, 112 allow_nan_stats=allow_nan_stats, 113 validate_args=validate_args, 114 name=name) 115 self._parameters = parameters 116 self._graph_parents += [self._rate] 117 118 @staticmethod 119 def _param_shapes(sample_shape): 120 return {"rate": ops.convert_to_tensor(sample_shape, dtype=dtypes.int32)} 121 122 @property 123 def rate(self): 124 return self._rate 125 126 def _log_survival_function(self, value): 127 return self._log_prob(value) - math_ops.log(self._rate) 128 129 def _sample_n(self, n, seed=None): 130 shape = array_ops.concat([[n], array_ops.shape(self._rate)], 0) 131 # Uniform variates must be sampled from the open-interval `(0, 1)` rather 132 # than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_dtype).tiny` 133 # because it is the smallest, positive, "normal" number. A "normal" number 134 # is such that the mantissa has an implicit leading 1. Normal, positive 135 # numbers x, y have the reasonable property that, `x + y >= max(x, y)`. In 136 # this case, a subnormal number (i.e., np.nextafter) can cause us to sample 137 # 0. 138 sampled = random_ops.random_uniform( 139 shape, 140 minval=np.finfo(self.dtype.as_numpy_dtype).tiny, 141 maxval=1., 142 seed=seed, 143 dtype=self.dtype) 144 return -math_ops.log(sampled) / self._rate 145 146 147class ExponentialWithSoftplusRate(Exponential): 148 """Exponential with softplus transform on `rate`.""" 149 150 @deprecation.deprecated( 151 "2019-01-01", 152 "Use `tfd.Exponential(tf.nn.softplus(rate)).", 153 warn_once=True) 154 def __init__(self, 155 rate, 156 validate_args=False, 157 allow_nan_stats=True, 158 name="ExponentialWithSoftplusRate"): 159 parameters = dict(locals()) 160 with ops.name_scope(name, values=[rate]) as name: 161 super(ExponentialWithSoftplusRate, self).__init__( 162 rate=nn.softplus(rate, name="softplus_rate"), 163 validate_args=validate_args, 164 allow_nan_stats=allow_nan_stats, 165 name=name) 166 self._parameters = parameters 167