pytorch

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# mypy: allow-untyped-defs
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from numbers import Number
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import torch
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from torch.distributions import constraints
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from torch.distributions.distribution import Distribution
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from torch.distributions.utils import broadcast_all
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from torch.types import _size
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__all__ = ["Laplace"]
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class Laplace(Distribution):
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    r"""
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    Creates a Laplace distribution parameterized by :attr:`loc` and :attr:`scale`.
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    Example::
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        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
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        >>> m = Laplace(torch.tensor([0.0]), torch.tensor([1.0]))
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        >>> m.sample()  # Laplace distributed with loc=0, 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
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        scale (float or Tensor): scale 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.real
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    has_rsample = True
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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 variance(self):
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        return 2 * self.scale.pow(2)
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    @property
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    def stddev(self):
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        return (2**0.5) * self.scale
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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(Laplace, _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(Laplace, 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 rsample(self, sample_shape: _size = torch.Size()) -> torch.Tensor:
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        shape = self._extended_shape(sample_shape)
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        finfo = torch.finfo(self.loc.dtype)
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        if torch._C._get_tracing_state():
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            # [JIT WORKAROUND] lack of support for .uniform_()
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            u = torch.rand(shape, dtype=self.loc.dtype, device=self.loc.device) * 2 - 1
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            return self.loc - self.scale * u.sign() * torch.log1p(
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                -u.abs().clamp(min=finfo.tiny)
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            )
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        u = self.loc.new(shape).uniform_(finfo.eps - 1, 1)
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        # TODO: If we ever implement tensor.nextafter, below is what we want ideally.
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        # u = self.loc.new(shape).uniform_(self.loc.nextafter(-.5, 0), .5)
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        return self.loc - self.scale * u.sign() * torch.log1p(-u.abs())
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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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        return -torch.log(2 * self.scale) - torch.abs(value - self.loc) / self.scale
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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 - 0.5 * (value - self.loc).sign() * torch.expm1(
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            -(value - self.loc).abs() / self.scale
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        )
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    def icdf(self, value):
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        term = value - 0.5
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        return self.loc - self.scale * (term).sign() * torch.log1p(-2 * term.abs())
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    def entropy(self):
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        return 1 + torch.log(2 * self.scale)
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