import torch
from torch.distributions import constraints
from torch.distributions.categorical import Categorical
from torch.distributions.distribution import Distribution


class OneHotCategorical(Distribution):
    r"""
    Creates a one-hot categorical distribution parameterized by :attr:`probs` or
    :attr:`logits`.

    Samples are one-hot coded vectors of size ``probs.size(-1)``.

    .. note:: The `probs` argument must be non-negative, finite and have a non-zero sum,
              and it will be normalized to sum to 1 along the last dimension. attr:`probs`
              will return this normalized value.
              The `logits` argument will be interpreted as unnormalized log probabilities
              and can therefore be any real number. It will likewise be normalized so that
              the resulting probabilities sum to 1 along the last dimension. attr:`logits`
              will return this normalized value.

    See also: :func:`torch.distributions.Categorical` for specifications of
    :attr:`probs` and :attr:`logits`.

    Example::

        >>> m = OneHotCategorical(torch.tensor([ 0.25, 0.25, 0.25, 0.25 ]))
        >>> m.sample()  # equal probability of 0, 1, 2, 3
        tensor([ 0.,  0.,  0.,  1.])

    Args:
        probs (Tensor): event probabilities
        logits (Tensor): event log probabilities (unnormalized)
    """
    arg_constraints = {'probs': constraints.simplex,
                       'logits': constraints.real_vector}
    support = constraints.one_hot
    has_enumerate_support = True

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

    def expand(self, batch_shape, _instance=None):
        new = self._get_checked_instance(OneHotCategorical, _instance)
        batch_shape = torch.Size(batch_shape)
        new._categorical = self._categorical.expand(batch_shape)
        super(OneHotCategorical, 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(self):
        return self._categorical._param

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

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

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

    @property
    def variance(self):
        return self._categorical.probs * (1 - self._categorical.probs)

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

    def sample(self, sample_shape=torch.Size()):
        sample_shape = torch.Size(sample_shape)
        probs = self._categorical.probs
        num_events = self._categorical._num_events
        indices = self._categorical.sample(sample_shape)
        return torch.nn.functional.one_hot(indices, num_events).to(probs)

    def log_prob(self, value):
        if self._validate_args:
            self._validate_sample(value)
        indices = value.max(-1)[1]
        return self._categorical.log_prob(indices)

    def entropy(self):
        return self._categorical.entropy()

    def enumerate_support(self, expand=True):
        n = self.event_shape[0]
        values = torch.eye(n, dtype=self._param.dtype, device=self._param.device)
        values = values.view((n,) + (1,) * len(self.batch_shape) + (n,))
        if expand:
            values = values.expand((n,) + self.batch_shape + (n,))
        return values

class OneHotCategoricalStraightThrough(OneHotCategorical):
    r"""
    Creates a reparameterizable :class:`OneHotCategorical` distribution based on the straight-
    through gradient estimator from [1].

    [1] Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation
    (Bengio et al, 2013)
    """
    has_rsample = True

    def rsample(self, sample_shape=torch.Size()):
        samples = self.sample(sample_shape)
        probs = self._categorical.probs  # cached via @lazy_property
        return samples + (probs - probs.detach())