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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 | |
| def mean(self): | |
| return self.loc | |
| def mode(self): | |
| return self.loc | |
| def stddev(self): | |
| return self.scale | |
| 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) | |
| 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) | |