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- # mypy: allow-untyped-defs
- import math
- from typing import Optional, Union
- import torch
- from torch import inf, Tensor
- from torch.distributions import constraints
- from torch.distributions.cauchy import Cauchy
- from torch.distributions.transformed_distribution import TransformedDistribution
- from torch.distributions.transforms import AbsTransform
- __all__ = ["HalfCauchy"]
- class HalfCauchy(TransformedDistribution):
- r"""
- Creates a half-Cauchy distribution parameterized by `scale` where::
- X ~ Cauchy(0, scale)
- Y = |X| ~ HalfCauchy(scale)
- Example::
- >>> # xdoctest: +IGNORE_WANT("non-deterministic")
- >>> m = HalfCauchy(torch.tensor([1.0]))
- >>> m.sample() # half-cauchy distributed with scale=1
- tensor([ 2.3214])
- Args:
- scale (float or Tensor): scale of the full Cauchy distribution
- """
- arg_constraints = {"scale": constraints.positive}
- support = constraints.nonnegative
- has_rsample = True
- base_dist: Cauchy
- def __init__(
- self,
- scale: Union[Tensor, float],
- validate_args: Optional[bool] = None,
- ) -> None:
- base_dist = Cauchy(0, scale, validate_args=False)
- super().__init__(base_dist, AbsTransform(), validate_args=validate_args)
- def expand(self, batch_shape, _instance=None):
- new = self._get_checked_instance(HalfCauchy, _instance)
- return super().expand(batch_shape, _instance=new)
- @property
- def scale(self) -> Tensor:
- return self.base_dist.scale
- @property
- def mean(self) -> Tensor:
- return torch.full(
- self._extended_shape(),
- math.inf,
- dtype=self.scale.dtype,
- device=self.scale.device,
- )
- @property
- def mode(self) -> Tensor:
- return torch.zeros_like(self.scale)
- @property
- def variance(self) -> Tensor:
- return self.base_dist.variance
- def log_prob(self, value):
- if self._validate_args:
- self._validate_sample(value)
- value = torch.as_tensor(
- value, dtype=self.base_dist.scale.dtype, device=self.base_dist.scale.device
- )
- log_prob = self.base_dist.log_prob(value) + math.log(2)
- log_prob = torch.where(value >= 0, log_prob, -inf)
- return log_prob
- def cdf(self, value):
- if self._validate_args:
- self._validate_sample(value)
- return 2 * self.base_dist.cdf(value) - 1
- def icdf(self, prob):
- return self.base_dist.icdf((prob + 1) / 2)
- def entropy(self):
- return self.base_dist.entropy() - math.log(2)
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