pytorch

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from torch.distributions import constraints
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from torch.distributions.normal import Normal
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from torch.distributions.transformed_distribution import TransformedDistribution
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from torch.distributions.transforms import ExpTransform
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__all__ = ["LogNormal"]
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class LogNormal(TransformedDistribution):
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    r"""
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    Creates a log-normal distribution parameterized by
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    :attr:`loc` and :attr:`scale` where::
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        X ~ Normal(loc, scale)
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        Y = exp(X) ~ LogNormal(loc, scale)
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    Example::
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        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
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        >>> m = LogNormal(torch.tensor([0.0]), torch.tensor([1.0]))
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        >>> m.sample()  # log-normal distributed with mean=0 and stddev=1
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        tensor([ 0.1046])
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    Args:
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        loc (float or Tensor): mean of log of distribution
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        scale (float or Tensor): standard deviation of log of the distribution
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    """
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    arg_constraints = {"loc": constraints.real, "scale": constraints.positive}
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    support = constraints.positive
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    has_rsample = True
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    def __init__(self, loc, scale, validate_args=None):
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        base_dist = Normal(loc, scale, validate_args=validate_args)
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        super().__init__(base_dist, ExpTransform(), validate_args=validate_args)
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    def expand(self, batch_shape, _instance=None):
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        new = self._get_checked_instance(LogNormal, _instance)
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        return super().expand(batch_shape, _instance=new)
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    @property
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    def loc(self):
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        return self.base_dist.loc
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    @property
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    def scale(self):
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        return self.base_dist.scale
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    @property
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    def mean(self):
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        return (self.loc + self.scale.pow(2) / 2).exp()
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    @property
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    def mode(self):
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        return (self.loc - self.scale.square()).exp()
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    @property
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    def variance(self):
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        scale_sq = self.scale.pow(2)
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        return scale_sq.expm1() * (2 * self.loc + scale_sq).exp()
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    def entropy(self):
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        return self.base_dist.entropy() + self.loc
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