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import math
from torch._six import inf, nan
from numbers import Number
import torch
from torch.distributions import constraints
from torch.distributions.distribution import Distribution
from torch.distributions.utils import broadcast_all
__all__ = ['Cauchy']
class Cauchy(Distribution):
r"""
Samples from a Cauchy (Lorentz) distribution. The distribution of the ratio of
independent normally distributed random variables with means `0` follows a
Cauchy distribution.
Example::
>>> # xdoctest: +IGNORE_WANT("non-deterinistic")
>>> m = Cauchy(torch.tensor([0.0]), torch.tensor([1.0]))
>>> m.sample() # sample from a Cauchy distribution with loc=0 and scale=1
tensor([ 2.3214])
Args:
loc (float or Tensor): mode or median of the distribution.
scale (float or Tensor): half width at half maximum.
"""
arg_constraints = {'loc': constraints.real, 'scale': constraints.positive}
support = constraints.real
has_rsample = True
def __init__(self, loc, scale, validate_args=None):
self.loc, self.scale = broadcast_all(loc, scale)
if isinstance(loc, Number) and isinstance(scale, Number):
batch_shape = torch.Size()
else:
batch_shape = self.loc.size()
super(Cauchy, self).__init__(batch_shape, validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Cauchy, _instance)
batch_shape = torch.Size(batch_shape)
new.loc = self.loc.expand(batch_shape)
new.scale = self.scale.expand(batch_shape)
super(Cauchy, new).__init__(batch_shape, validate_args=False)
new._validate_args = self._validate_args
return new
@property
def mean(self):
return torch.full(self._extended_shape(), nan, dtype=self.loc.dtype, device=self.loc.device)
@property
def mode(self):
return self.loc
@property
def variance(self):
return torch.full(self._extended_shape(), inf, dtype=self.loc.dtype, device=self.loc.device)
def rsample(self, sample_shape=torch.Size()):
shape = self._extended_shape(sample_shape)
eps = self.loc.new(shape).cauchy_()
return self.loc + eps * self.scale
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
return -math.log(math.pi) - self.scale.log() - (1 + ((value - self.loc) / self.scale)**2).log()
def cdf(self, value):
if self._validate_args:
self._validate_sample(value)
return torch.atan((value - self.loc) / self.scale) / math.pi + 0.5
def icdf(self, value):
return torch.tan(math.pi * (value - 0.5)) * self.scale + self.loc
def entropy(self):
return math.log(4 * math.pi) + self.scale.log()
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