Source code for torch.distributions.cauchy

import math
from numbers import Number

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

__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): 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().__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): 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 )
[docs] def rsample(self, sample_shape=torch.Size()): shape = self._extended_shape(sample_shape) eps = 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) return torch.atan((value - self.loc) / self.scale) / math.pi + 0.5
[docs] def icdf(self, value): return torch.tan(math.pi * (value - 0.5)) * self.scale + self.loc
[docs] def entropy(self): return math.log(4 * math.pi) + self.scale.log()


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