from torch.nn.modules.distance import PairwiseDistance
import sympy
from .losses import Divergence
from ..utils import get_dict_values


class WassersteinDistance(Divergence):
    r"""
    Wasserstein distance.

    .. math::

         W(p, q) = \inf_{\Gamma \in \mathcal{P}(x_p\sim p, x_q\sim q)} \mathbb{E}_{(x_p, x_q) \sim \Gamma}[d(x_p, x_q)]

    However, instead of the above true distance, this class computes the following one.

    .. math::

         W'(p, q) = \mathbb{E}_{x_p\sim p, x_q \sim q}[d(x_p, x_q)].


    Here, :math:`W'` is the upper of :math:`W` (i.e., :math:`W\leq W'`), and these are equal when both :math:`p`
    and :math:`q` are degenerate (deterministic) distributions.

    Examples
    --------
    >>> import torch
    >>> from pixyz.distributions import Normal
    >>> p = Normal(loc="x", scale=torch.tensor(1.), var=["z"], cond_var=["x"], features_shape=[64], name="p")
    >>> q = Normal(loc="x", scale=torch.tensor(1.), var=["z"], cond_var=["x"], features_shape=[64], name="q")
    >>> loss_cls = WassersteinDistance(p, q)
    >>> print(loss_cls)
    W^{upper} \left(p(z|x), q(z|x) \right)
    >>> loss = loss_cls.eval({"x": torch.randn(1, 64)})
    """

    def __init__(self, p, q, metric=PairwiseDistance(p=2)):
        if set(p.var) != set(q.var):
            raise ValueError("The two distribution variables must be the same.")

        if len(p.var) != 1:
            raise ValueError("A given distribution must have only one variable.")

        super().__init__(p, q)

        if len(p.input_var) > 0:
            self.input_dist = p
        elif len(q.input_var) > 0:
            self.input_dist = q
        else:
            raise NotImplementedError()

        self.metric = metric

    @property
    def _symbol(self):
        return sympy.Symbol("W^{{upper}} \\left({}, {} \\right)".format(self.p.prob_text, self.q.prob_text))

    def _get_batch_n(self, x_dict):
        return get_dict_values(x_dict, self.input_dist.input_var[0])[0].shape[0]

    def forward(self, x_dict, **kwargs):
        batch_n = self._get_batch_n(x_dict)

        # sample from distributions
        p_x = get_dict_values(self.p.sample(x_dict, batch_n=batch_n, **kwargs), self.p.var)[0]
        q_x = get_dict_values(self.q.sample(x_dict, batch_n=batch_n, **kwargs), self.q.var)[0]

        if p_x.shape != q_x.shape:
            raise ValueError("The two distribution variables must have the same shape.")

        distance = self.metric(p_x, q_x)

        return distance, {}
