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# Source code for torch.distributions.exponential

    from numbers import Number

    import torch
    from torch.distributions import constraints
    from torch.distributions.exp_family import ExponentialFamily
    from torch.distributions.utils import broadcast_all

    __all__ = ["Exponential"]

    class Exponential(ExponentialFamily):
        r"""
        Creates a Exponential distribution parameterized by :attr:`rate`.

        Example::

            >>> # xdoctest: +IGNORE_WANT("non-deterinistic")
            >>> m = Exponential(torch.tensor([1.0]))
            >>> m.sample()  # Exponential distributed with rate=1
            tensor([ 0.1046])

        Args:
            rate (float or Tensor): rate = 1 / scale of the distribution
        """
        arg_constraints = {"rate": constraints.positive}
        support = constraints.nonnegative
        has_rsample = True
        _mean_carrier_measure = 0

        @property
        def mean(self):
            return self.rate.reciprocal()

        @property
        def mode(self):
            return torch.zeros_like(self.rate)

        @property
        def stddev(self):
            return self.rate.reciprocal()

        @property
        def variance(self):
            return self.rate.pow(-2)

        def __init__(self, rate, validate_args=None):
            (self.rate,) = broadcast_all(rate)
            batch_shape = torch.Size() if isinstance(rate, Number) else self.rate.size()
            super().__init__(batch_shape, validate_args=validate_args)

        def expand(self, batch_shape, _instance=None):
            new = self._get_checked_instance(Exponential, _instance)
            batch_shape = torch.Size(batch_shape)
            new.rate = self.rate.expand(batch_shape)
            super(Exponential, new).__init__(batch_shape, validate_args=False)
            new._validate_args = self._validate_args
            return new

        def rsample(self, sample_shape=torch.Size()):
            shape = self._extended_shape(sample_shape)
            return self.rate.new(shape).exponential_() / self.rate

        def log_prob(self, value):
            if self._validate_args:
                self._validate_sample(value)
            return self.rate.log() - self.rate * value

        def cdf(self, value):
            if self._validate_args:
                self._validate_sample(value)
            return 1 - torch.exp(-self.rate * value)

        def icdf(self, value):
            return -torch.log1p(-value) / self.rate

        def entropy(self):
            return 1.0 - torch.log(self.rate)

        @property
        def _natural_params(self):
            return (-self.rate,)

        def _log_normalizer(self, x):
            return -torch.log(-x)

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