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