File size: 3,028 Bytes
9c6594c |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 |
# mypy: allow-untyped-defs
import math
import torch
from torch import inf, nan, Tensor
from torch.distributions import constraints
from torch.distributions.distribution import Distribution
from torch.distributions.utils import broadcast_all
from torch.types import _Number, _size
__all__ = ["Cauchy"]
class Cauchy(Distribution):
r"""
Samples from a Cauchy (Lorentz) distribution. The distribution of the ratio of
independent normally distributed random variables with means `0` follows a
Cauchy distribution.
Example::
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = Cauchy(torch.tensor([0.0]), torch.tensor([1.0]))
>>> m.sample() # sample from a Cauchy distribution with loc=0 and scale=1
tensor([ 2.3214])
Args:
loc (float or Tensor): mode or median of the distribution.
scale (float or Tensor): half width at half maximum.
"""
arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
support = constraints.real
has_rsample = True
def __init__(self, loc, scale, validate_args=None):
self.loc, self.scale = broadcast_all(loc, scale)
if isinstance(loc, _Number) and isinstance(scale, _Number):
batch_shape = torch.Size()
else:
batch_shape = self.loc.size()
super().__init__(batch_shape, validate_args=validate_args)
def expand(self, batch_shape, _instance=None):
new = self._get_checked_instance(Cauchy, _instance)
batch_shape = torch.Size(batch_shape)
new.loc = self.loc.expand(batch_shape)
new.scale = self.scale.expand(batch_shape)
super(Cauchy, new).__init__(batch_shape, validate_args=False)
new._validate_args = self._validate_args
return new
@property
def mean(self) -> Tensor:
return torch.full(
self._extended_shape(), nan, dtype=self.loc.dtype, device=self.loc.device
)
@property
def mode(self) -> Tensor:
return self.loc
@property
def variance(self) -> Tensor:
return torch.full(
self._extended_shape(), inf, dtype=self.loc.dtype, device=self.loc.device
)
def rsample(self, sample_shape: _size = torch.Size()) -> Tensor:
shape = self._extended_shape(sample_shape)
eps = self.loc.new(shape).cauchy_()
return self.loc + eps * self.scale
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
return (
-math.log(math.pi)
- self.scale.log()
- (((value - self.loc) / self.scale) ** 2).log1p()
)
def cdf(self, value):
if self._validate_args:
self._validate_sample(value)
return torch.atan((value - self.loc) / self.scale) / math.pi + 0.5
def icdf(self, value):
return torch.tan(math.pi * (value - 0.5)) * self.scale + self.loc
def entropy(self):
return math.log(4 * math.pi) + self.scale.log()
|