91 lines
2.9 KiB
Python
91 lines
2.9 KiB
Python
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import math
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from numbers import Number
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import torch
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from torch import inf, nan
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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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__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):
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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):
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return self.loc
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@property
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def variance(self):
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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=torch.Size()):
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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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