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# Source code for torch.distributions.relaxed_categorical

    import torch
    from torch.distributions import constraints
    from torch.distributions.categorical import Categorical
    from torch.distributions.distribution import Distribution
    from torch.distributions.transformed_distribution import TransformedDistribution
    from torch.distributions.transforms import ExpTransform
    from torch.distributions.utils import broadcast_all, clamp_probs

    __all__ = ["ExpRelaxedCategorical", "RelaxedOneHotCategorical"]

    class ExpRelaxedCategorical(Distribution):
        r"""
        Creates a ExpRelaxedCategorical parameterized by
        :attr:`temperature`, and either :attr:`probs` or :attr:`logits` (but not both).
        Returns the log of a point in the simplex. Based on the interface to
        :class:`OneHotCategorical`.

        Implementation based on [1].

        See also: :func:`torch.distributions.OneHotCategorical`

        Args:
            temperature (Tensor): relaxation temperature
            probs (Tensor): event probabilities
            logits (Tensor): unnormalized log probability for each event

        [1] The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables
        (Maddison et al, 2017)

        [2] Categorical Reparametrization with Gumbel-Softmax
        (Jang et al, 2017)
        """
        arg_constraints = {"probs": constraints.simplex, "logits": constraints.real_vector}
        support = (
            constraints.real_vector
        )  # The true support is actually a submanifold of this.
        has_rsample = True

        def __init__(self, temperature, probs=None, logits=None, validate_args=None):
            self._categorical = Categorical(probs, logits)
            self.temperature = temperature
            batch_shape = self._categorical.batch_shape
            event_shape = self._categorical.param_shape[-1:]
            super().__init__(batch_shape, event_shape, validate_args=validate_args)

        def expand(self, batch_shape, _instance=None):
            new = self._get_checked_instance(ExpRelaxedCategorical, _instance)
            batch_shape = torch.Size(batch_shape)
            new.temperature = self.temperature
            new._categorical = self._categorical.expand(batch_shape)
            super(ExpRelaxedCategorical, new).__init__(
                batch_shape, self.event_shape, validate_args=False
            )
            new._validate_args = self._validate_args
            return new

        def _new(self, *args, **kwargs):
            return self._categorical._new(*args, **kwargs)

        @property
        def param_shape(self):
            return self._categorical.param_shape

        @property
        def logits(self):
            return self._categorical.logits

        @property
        def probs(self):
            return self._categorical.probs

        def rsample(self, sample_shape=torch.Size()):
            shape = self._extended_shape(sample_shape)
            uniforms = clamp_probs(
                torch.rand(shape, dtype=self.logits.dtype, device=self.logits.device)
            )
            gumbels = -((-(uniforms.log())).log())
            scores = (self.logits + gumbels) / self.temperature
            return scores - scores.logsumexp(dim=-1, keepdim=True)

        def log_prob(self, value):
            K = self._categorical._num_events
            if self._validate_args:
                self._validate_sample(value)
            logits, value = broadcast_all(self.logits, value)
            log_scale = torch.full_like(
                self.temperature, float(K)
            ).lgamma() - self.temperature.log().mul(-(K - 1))
            score = logits - value.mul(self.temperature)
            score = (score - score.logsumexp(dim=-1, keepdim=True)).sum(-1)
            return score + log_scale

    class RelaxedOneHotCategorical(TransformedDistribution):
        r"""
        Creates a RelaxedOneHotCategorical distribution parametrized by
        :attr:`temperature`, and either :attr:`probs` or :attr:`logits`.
        This is a relaxed version of the :class:`OneHotCategorical` distribution, so
        its samples are on simplex, and are reparametrizable.

        Example::

            >>> # xdoctest: +IGNORE_WANT("non-deterinistic")
            >>> m = RelaxedOneHotCategorical(torch.tensor([2.2]),
            ...                              torch.tensor([0.1, 0.2, 0.3, 0.4]))
            >>> m.sample()
            tensor([ 0.1294,  0.2324,  0.3859,  0.2523])

        Args:
            temperature (Tensor): relaxation temperature
            probs (Tensor): event probabilities
            logits (Tensor): unnormalized log probability for each event
        """
        arg_constraints = {"probs": constraints.simplex, "logits": constraints.real_vector}
        support = constraints.simplex
        has_rsample = True

        def __init__(self, temperature, probs=None, logits=None, validate_args=None):
            base_dist = ExpRelaxedCategorical(
                temperature, probs, logits, validate_args=validate_args
            )
            super().__init__(base_dist, ExpTransform(), validate_args=validate_args)

        def expand(self, batch_shape, _instance=None):
            new = self._get_checked_instance(RelaxedOneHotCategorical, _instance)
            return super().expand(batch_shape, _instance=new)

        @property
        def temperature(self):
            return self.base_dist.temperature

        @property
        def logits(self):
            return self.base_dist.logits

        @property
        def probs(self):
            return self.base_dist.probs

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