1# mypy: allow-untyped-defs 2import math 3 4import torch 5from torch import inf 6from torch.distributions import constraints 7from torch.distributions.cauchy import Cauchy 8from torch.distributions.transformed_distribution import TransformedDistribution 9from torch.distributions.transforms import AbsTransform 10 11 12__all__ = ["HalfCauchy"] 13 14 15class HalfCauchy(TransformedDistribution): 16 r""" 17 Creates a half-Cauchy distribution parameterized by `scale` where:: 18 19 X ~ Cauchy(0, scale) 20 Y = |X| ~ HalfCauchy(scale) 21 22 Example:: 23 24 >>> # xdoctest: +IGNORE_WANT("non-deterministic") 25 >>> m = HalfCauchy(torch.tensor([1.0])) 26 >>> m.sample() # half-cauchy distributed with scale=1 27 tensor([ 2.3214]) 28 29 Args: 30 scale (float or Tensor): scale of the full Cauchy distribution 31 """ 32 arg_constraints = {"scale": constraints.positive} 33 support = constraints.nonnegative 34 has_rsample = True 35 36 def __init__(self, scale, validate_args=None): 37 base_dist = Cauchy(0, scale, validate_args=False) 38 super().__init__(base_dist, AbsTransform(), validate_args=validate_args) 39 40 def expand(self, batch_shape, _instance=None): 41 new = self._get_checked_instance(HalfCauchy, _instance) 42 return super().expand(batch_shape, _instance=new) 43 44 @property 45 def scale(self): 46 return self.base_dist.scale 47 48 @property 49 def mean(self): 50 return torch.full( 51 self._extended_shape(), 52 math.inf, 53 dtype=self.scale.dtype, 54 device=self.scale.device, 55 ) 56 57 @property 58 def mode(self): 59 return torch.zeros_like(self.scale) 60 61 @property 62 def variance(self): 63 return self.base_dist.variance 64 65 def log_prob(self, value): 66 if self._validate_args: 67 self._validate_sample(value) 68 value = torch.as_tensor( 69 value, dtype=self.base_dist.scale.dtype, device=self.base_dist.scale.device 70 ) 71 log_prob = self.base_dist.log_prob(value) + math.log(2) 72 log_prob = torch.where(value >= 0, log_prob, -inf) 73 return log_prob 74 75 def cdf(self, value): 76 if self._validate_args: 77 self._validate_sample(value) 78 return 2 * self.base_dist.cdf(value) - 1 79 80 def icdf(self, prob): 81 return self.base_dist.icdf((prob + 1) / 2) 82 83 def entropy(self): 84 return self.base_dist.entropy() - math.log(2) 85