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# Source code for torch.distributions.cauchy

# mypy: allow-untyped-defs
import math
from numbers import Number

import torch
from torch import inf, nan
from torch.distributions import constraints
from torch.distributions.distribution import Distribution

__all__ = ["Cauchy"]

[docs]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-deterministic")
>>> 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):
if isinstance(loc, Number) and isinstance(scale, Number):
batch_shape = torch.Size()
else:
batch_shape = self.loc.size()
super().__init__(batch_shape, validate_args=validate_args)

[docs]    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):
self._extended_shape(), nan, dtype=self.loc.dtype, device=self.loc.device
)

@property
def mode(self):
return self.loc

@property
def variance(self):
self._extended_shape(), inf, dtype=self.loc.dtype, device=self.loc.device
)

[docs]    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

[docs]    def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
return (
-math.log(math.pi)
- self.scale.log()
- (((value - self.loc) / self.scale) ** 2).log1p()
)

[docs]    def cdf(self, value):
if self._validate_args:
self._validate_sample(value)

[docs]    def icdf(self, value):

[docs]    def entropy(self):
return math.log(4 * math.pi) + self.scale.log()


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