| 12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152535455565758596061626364656667686970717273747576777879 |
- 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
- 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::
- >>> 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()
|
