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| 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"] | |
| 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) | |
| 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 | |
| def mean(self): | |
| return torch.full( | |
| self._extended_shape(), nan, dtype=self.loc.dtype, device=self.loc.device | |
| ) | |
| def mode(self): | |
| return self.loc | |
| 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() | |
| - (((value - self.loc) / self.scale) ** 2).log1p() | |
| ) | |
| 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() | |