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# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# 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.
# ==============================================================================
"""The Exponential distribution class."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import numpy as np
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn
from tensorflow.python.ops import random_ops
from tensorflow.python.ops.distributions import gamma
__all__ = [
"Exponential",
"ExponentialWithSoftplusRate",
]
class Exponential(gamma.Gamma):
"""Exponential distribution.
The Exponential distribution is parameterized by an event `rate` parameter.
#### Mathematical Details
The probability density function (pdf) is,
```none
pdf(x; lambda, x > 0) = exp(-lambda x) / Z
Z = 1 / lambda
```
where `rate = lambda` and `Z` is the normalizaing constant.
The Exponential distribution is a special case of the Gamma distribution,
i.e.,
```python
Exponential(rate) = Gamma(concentration=1., rate)
```
The Exponential distribution uses a `rate` parameter, or "inverse scale",
which can be intuited as,
```none
X ~ Exponential(rate=1)
Y = X / rate
```
"""
def __init__(self,
rate,
validate_args=False,
allow_nan_stats=True,
name="Exponential"):
"""Construct Exponential distribution with parameter `rate`.
Args:
rate: Floating point tensor, equivalent to `1 / mean`. Must contain only
positive values.
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 = locals()
# Even though all statistics of are defined for valid inputs, this is not
# true in the parent class "Gamma." Therefore, passing
# allow_nan_stats=True
# through to the parent class results in unnecessary asserts.
with ops.name_scope(name, values=[rate]):
self._rate = ops.convert_to_tensor(rate, name="rate")
super(Exponential, self).__init__(
concentration=array_ops.ones([], dtype=self._rate.dtype),
rate=self._rate,
allow_nan_stats=allow_nan_stats,
validate_args=validate_args,
name=name)
# While the Gamma distribution is not reparameterizable, the exponential
# distribution is.
self._reparameterization_type = True
self._parameters = parameters
self._graph_parents += [self._rate]
@staticmethod
def _param_shapes(sample_shape):
return {"rate": ops.convert_to_tensor(sample_shape, dtype=dtypes.int32)}
@property
def rate(self):
return self._rate
def _sample_n(self, n, seed=None):
shape = array_ops.concat([[n], array_ops.shape(self._rate)], 0)
# Uniform variates must be sampled from the open-interval `(0, 1)` rather
# than `[0, 1)`. To do so, we use `np.finfo(self.dtype.as_numpy_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.
sampled = random_ops.random_uniform(
shape,
minval=np.finfo(self.dtype.as_numpy_dtype).tiny,
maxval=1.,
seed=seed,
dtype=self.dtype)
return -math_ops.log(sampled) / self._rate
class ExponentialWithSoftplusRate(Exponential):
"""Exponential with softplus transform on `rate`."""
def __init__(self,
rate,
validate_args=False,
allow_nan_stats=True,
name="ExponentialWithSoftplusRate"):
parameters = locals()
with ops.name_scope(name, values=[rate]):
super(ExponentialWithSoftplusRate, self).__init__(
rate=nn.softplus(rate, name="softplus_rate"),
validate_args=validate_args,
allow_nan_stats=allow_nan_stats,
name=name)
self._parameters = parameters
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