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from numbers import Number
import torch
from torch.distributions import constraints
from torch.distributions.exp_family import ExponentialFamily
from torch.distributions.utils import broadcast_all
__all__ = ["Exponential"]
class Exponential(ExponentialFamily):
r"""
Creates a Exponential distribution parameterized by :attr:`rate`.
Example::
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = Exponential(torch.tensor([1.0]))
>>> m.sample() # Exponential distributed with rate=1
tensor([ 0.1046])
Args:
rate (float or Tensor): rate = 1 / scale of the distribution
"""
arg_constraints = {"rate": constraints.positive}
support = constraints.nonnegative
has_rsample = True
_mean_carrier_measure = 0
@property
def mean(self):
return self.rate.reciprocal()
@property
def mode(self):
return torch.zeros_like(self.rate)
@property
def stddev(self):
return self.rate.reciprocal()
@property
def variance(self):
return self.rate.pow(-2)
def __init__(self, rate, validate_args=None):
(self.rate,) = broadcast_all(rate)
batch_shape = torch.Size() if isinstance(rate, Number) else self.rate.size()
super().__init__(batch_shape, validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Exponential, _instance)
batch_shape = torch.Size(batch_shape)
new.rate = self.rate.expand(batch_shape)
super(Exponential, new).__init__(batch_shape, validate_args=False)
new._validate_args = self._validate_args
return new
def rsample(self, sample_shape=torch.Size()):
shape = self._extended_shape(sample_shape)
return self.rate.new(shape).exponential_() / self.rate
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
return self.rate.log() - self.rate * value
def cdf(self, value):
if self._validate_args:
self._validate_sample(value)
return 1 - torch.exp(-self.rate * value)
def icdf(self, value):
return -torch.log1p(-value) / self.rate
def entropy(self):
return 1.0 - torch.log(self.rate)
@property
def _natural_params(self):
return (-self.rate,)
def _log_normalizer(self, x):
return -torch.log(-x)
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