pytorch

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# mypy: allow-untyped-defs
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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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from torch.types import _size
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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: _size = torch.Size()) -> torch.Tensor:
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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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