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import math
import torch
from torch import inf
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
def __init__(self, scale, validate_args=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):
return self.base_dist.scale
@property
def mean(self):
return torch.full(
self._extended_shape(),
math.inf,
dtype=self.scale.dtype,
device=self.scale.device,
)
@property
def mode(self):
return torch.zeros_like(self.scale)
@property
def variance(self):
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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