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import math |
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import torch |
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from torch import inf, nan, Tensor |
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from torch.distributions import constraints |
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from torch.distributions.distribution import Distribution |
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from torch.distributions.utils import broadcast_all |
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from torch.types import _Number, _size |
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__all__ = ["Cauchy"] |
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class Cauchy(Distribution): |
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r""" |
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Samples from a Cauchy (Lorentz) distribution. The distribution of the ratio of |
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independent normally distributed random variables with means `0` follows a |
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Cauchy distribution. |
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Example:: |
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>>> # xdoctest: +IGNORE_WANT("non-deterministic") |
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>>> m = Cauchy(torch.tensor([0.0]), torch.tensor([1.0])) |
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>>> m.sample() # sample from a Cauchy distribution with loc=0 and scale=1 |
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tensor([ 2.3214]) |
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Args: |
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loc (float or Tensor): mode or median of the distribution. |
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scale (float or Tensor): half width at half maximum. |
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""" |
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arg_constraints = {"loc": constraints.real, "scale": constraints.positive} |
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support = constraints.real |
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has_rsample = True |
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def __init__(self, loc, scale, validate_args=None): |
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self.loc, self.scale = broadcast_all(loc, scale) |
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if isinstance(loc, _Number) and isinstance(scale, _Number): |
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batch_shape = torch.Size() |
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else: |
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batch_shape = self.loc.size() |
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super().__init__(batch_shape, validate_args=validate_args) |
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def expand(self, batch_shape, _instance=None): |
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new = self._get_checked_instance(Cauchy, _instance) |
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batch_shape = torch.Size(batch_shape) |
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new.loc = self.loc.expand(batch_shape) |
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new.scale = self.scale.expand(batch_shape) |
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super(Cauchy, new).__init__(batch_shape, validate_args=False) |
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new._validate_args = self._validate_args |
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return new |
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@property |
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def mean(self) -> Tensor: |
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return torch.full( |
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self._extended_shape(), nan, dtype=self.loc.dtype, device=self.loc.device |
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) |
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@property |
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def mode(self) -> Tensor: |
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return self.loc |
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@property |
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def variance(self) -> Tensor: |
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return torch.full( |
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self._extended_shape(), inf, dtype=self.loc.dtype, device=self.loc.device |
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) |
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def rsample(self, sample_shape: _size = torch.Size()) -> Tensor: |
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shape = self._extended_shape(sample_shape) |
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eps = self.loc.new(shape).cauchy_() |
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return self.loc + eps * self.scale |
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def log_prob(self, value): |
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if self._validate_args: |
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self._validate_sample(value) |
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return ( |
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-math.log(math.pi) |
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- self.scale.log() |
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- (((value - self.loc) / self.scale) ** 2).log1p() |
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) |
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def cdf(self, value): |
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if self._validate_args: |
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self._validate_sample(value) |
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return torch.atan((value - self.loc) / self.scale) / math.pi + 0.5 |
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def icdf(self, value): |
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return torch.tan(math.pi * (value - 0.5)) * self.scale + self.loc |
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def entropy(self): |
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return math.log(4 * math.pi) + self.scale.log() |
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