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import math
from numbers import Number, Real
import torch
from torch.distributions import constraints
from torch.distributions.exp_family import ExponentialFamily
from torch.distributions.utils import _standard_normal, broadcast_all
__all__ = ["Normal"]
class Normal(ExponentialFamily):
r"""
Creates a normal (also called Gaussian) distribution parameterized by
:attr:`loc` and :attr:`scale`.
Example::
>>> # xdoctest: +IGNORE_WANT("non-deterministic")
>>> m = Normal(torch.tensor([0.0]), torch.tensor([1.0]))
>>> m.sample() # normally distributed with loc=0 and scale=1
tensor([ 0.1046])
Args:
loc (float or Tensor): mean of the distribution (often referred to as mu)
scale (float or Tensor): standard deviation of the distribution
(often referred to as sigma)
"""
arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
support = constraints.real
has_rsample = True
_mean_carrier_measure = 0
@property
def mean(self):
return self.loc
@property
def mode(self):
return self.loc
@property
def stddev(self):
return self.scale
@property
def variance(self):
return self.stddev.pow(2)
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(Normal, _instance)
batch_shape = torch.Size(batch_shape)
new.loc = self.loc.expand(batch_shape)
new.scale = self.scale.expand(batch_shape)
super(Normal, new).__init__(batch_shape, validate_args=False)
new._validate_args = self._validate_args
return new
def sample(self, sample_shape=torch.Size()):
shape = self._extended_shape(sample_shape)
with torch.no_grad():
return torch.normal(self.loc.expand(shape), self.scale.expand(shape))
def rsample(self, sample_shape=torch.Size()):
shape = self._extended_shape(sample_shape)
eps = _standard_normal(shape, dtype=self.loc.dtype, device=self.loc.device)
return self.loc + eps * self.scale
def log_prob(self, value):
if self._validate_args:
self._validate_sample(value)
# compute the variance
var = self.scale**2
log_scale = (
math.log(self.scale) if isinstance(self.scale, Real) else self.scale.log()
)
return (
-((value - self.loc) ** 2) / (2 * var)
- log_scale
- math.log(math.sqrt(2 * math.pi))
)
def cdf(self, value):
if self._validate_args:
self._validate_sample(value)
return 0.5 * (
1 + torch.erf((value - self.loc) * self.scale.reciprocal() / math.sqrt(2))
)
def icdf(self, value):
return self.loc + self.scale * torch.erfinv(2 * value - 1) * math.sqrt(2)
def entropy(self):
return 0.5 + 0.5 * math.log(2 * math.pi) + torch.log(self.scale)
@property
def _natural_params(self):
return (self.loc / self.scale.pow(2), -0.5 * self.scale.pow(2).reciprocal())
def _log_normalizer(self, x, y):
return -0.25 * x.pow(2) / y + 0.5 * torch.log(-math.pi / y)
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