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# Source code for torch.distributions.fishersnedecor

    from numbers import Number

    import torch
    from torch import nan
    from torch.distributions import constraints
    from torch.distributions.distribution import Distribution
    from torch.distributions.gamma import Gamma
    from torch.distributions.utils import broadcast_all

    __all__ = ["FisherSnedecor"]

    class FisherSnedecor(Distribution):
        r"""
        Creates a Fisher-Snedecor distribution parameterized by :attr:`df1` and :attr:`df2`.

        Example::

            >>> # xdoctest: +IGNORE_WANT("non-deterinistic")
            >>> m = FisherSnedecor(torch.tensor([1.0]), torch.tensor([2.0]))
            >>> m.sample()  # Fisher-Snedecor-distributed with df1=1 and df2=2
            tensor([ 0.2453])

        Args:
            df1 (float or Tensor): degrees of freedom parameter 1
            df2 (float or Tensor): degrees of freedom parameter 2
        """
        arg_constraints = {"df1": constraints.positive, "df2": constraints.positive}
        support = constraints.positive
        has_rsample = True

        def __init__(self, df1, df2, validate_args=None):
            self.df1, self.df2 = broadcast_all(df1, df2)
            self._gamma1 = Gamma(self.df1 * 0.5, self.df1)
            self._gamma2 = Gamma(self.df2 * 0.5, self.df2)

            if isinstance(df1, Number) and isinstance(df2, Number):
                batch_shape = torch.Size()
            else:
                batch_shape = self.df1.size()
            super().__init__(batch_shape, validate_args=validate_args)

        def expand(self, batch_shape, _instance=None):
            new = self._get_checked_instance(FisherSnedecor, _instance)
            batch_shape = torch.Size(batch_shape)
            new.df1 = self.df1.expand(batch_shape)
            new.df2 = self.df2.expand(batch_shape)
            new._gamma1 = self._gamma1.expand(batch_shape)
            new._gamma2 = self._gamma2.expand(batch_shape)
            super(FisherSnedecor, new).__init__(batch_shape, validate_args=False)
            new._validate_args = self._validate_args
            return new

        @property
        def mean(self):
            df2 = self.df2.clone(memory_format=torch.contiguous_format)
            df2[df2 <= 2] = nan
            return df2 / (df2 - 2)

        @property
        def mode(self):
            mode = (self.df1 - 2) / self.df1 * self.df2 / (self.df2 + 2)
            mode[self.df1 <= 2] = nan
            return mode

        @property
        def variance(self):
            df2 = self.df2.clone(memory_format=torch.contiguous_format)
            df2[df2 <= 4] = nan
            return (
                2
                * df2.pow(2)
                * (self.df1 + df2 - 2)
                / (self.df1 * (df2 - 2).pow(2) * (df2 - 4))
            )

        def rsample(self, sample_shape=torch.Size(())):
            shape = self._extended_shape(sample_shape)
            #   X1 ~ Gamma(df1 / 2, 1 / df1), X2 ~ Gamma(df2 / 2, 1 / df2)
            #   Y = df2 * df1 * X1 / (df1 * df2 * X2) = X1 / X2 ~ F(df1, df2)
            X1 = self._gamma1.rsample(sample_shape).view(shape)
            X2 = self._gamma2.rsample(sample_shape).view(shape)
            tiny = torch.finfo(X2.dtype).tiny
            X2.clamp_(min=tiny)
            Y = X1 / X2
            Y.clamp_(min=tiny)
            return Y

        def log_prob(self, value):
            if self._validate_args:
                self._validate_sample(value)
            ct1 = self.df1 * 0.5
            ct2 = self.df2 * 0.5
            ct3 = self.df1 / self.df2
            t1 = (ct1 + ct2).lgamma() - ct1.lgamma() - ct2.lgamma()
            t2 = ct1 * ct3.log() + (ct1 - 1) * torch.log(value)
            t3 = (ct1 + ct2) * torch.log1p(ct3 * value)
            return t1 + t2 - t3

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