# mypy: allow-untyped-defs
from typing import Dict

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


__all__ = ["MixtureSameFamily"]


class MixtureSameFamily(Distribution):
    r"""
    The `MixtureSameFamily` distribution implements a (batch of) mixture
    distribution where all component are from different parameterizations of
    the same distribution type. It is parameterized by a `Categorical`
    "selecting distribution" (over `k` component) and a component
    distribution, i.e., a `Distribution` with a rightmost batch shape
    (equal to `[k]`) which indexes each (batch of) component.

    Examples::

        >>> # xdoctest: +SKIP("undefined vars")
        >>> # Construct Gaussian Mixture Model in 1D consisting of 5 equally
        >>> # weighted normal distributions
        >>> mix = D.Categorical(torch.ones(5,))
        >>> comp = D.Normal(torch.randn(5,), torch.rand(5,))
        >>> gmm = MixtureSameFamily(mix, comp)

        >>> # Construct Gaussian Mixture Model in 2D consisting of 5 equally
        >>> # weighted bivariate normal distributions
        >>> mix = D.Categorical(torch.ones(5,))
        >>> comp = D.Independent(D.Normal(
        ...          torch.randn(5,2), torch.rand(5,2)), 1)
        >>> gmm = MixtureSameFamily(mix, comp)

        >>> # Construct a batch of 3 Gaussian Mixture Models in 2D each
        >>> # consisting of 5 random weighted bivariate normal distributions
        >>> mix = D.Categorical(torch.rand(3,5))
        >>> comp = D.Independent(D.Normal(
        ...         torch.randn(3,5,2), torch.rand(3,5,2)), 1)
        >>> gmm = MixtureSameFamily(mix, comp)

    Args:
        mixture_distribution: `torch.distributions.Categorical`-like
            instance. Manages the probability of selecting component.
            The number of categories must match the rightmost batch
            dimension of the `component_distribution`. Must have either
            scalar `batch_shape` or `batch_shape` matching
            `component_distribution.batch_shape[:-1]`
        component_distribution: `torch.distributions.Distribution`-like
            instance. Right-most batch dimension indexes component.
    """
    arg_constraints: Dict[str, constraints.Constraint] = {}
    has_rsample = False

    def __init__(
        self, mixture_distribution, component_distribution, validate_args=None
    ):
        self._mixture_distribution = mixture_distribution
        self._component_distribution = component_distribution

        if not isinstance(self._mixture_distribution, Categorical):
            raise ValueError(
                " The Mixture distribution needs to be an "
                " instance of torch.distributions.Categorical"
            )

        if not isinstance(self._component_distribution, Distribution):
            raise ValueError(
                "The Component distribution need to be an "
                "instance of torch.distributions.Distribution"
            )

        # Check that batch size matches
        mdbs = self._mixture_distribution.batch_shape
        cdbs = self._component_distribution.batch_shape[:-1]
        for size1, size2 in zip(reversed(mdbs), reversed(cdbs)):
            if size1 != 1 and size2 != 1 and size1 != size2:
                raise ValueError(
                    f"`mixture_distribution.batch_shape` ({mdbs}) is not "
                    "compatible with `component_distribution."
                    f"batch_shape`({cdbs})"
                )

        # Check that the number of mixture component matches
        km = self._mixture_distribution.logits.shape[-1]
        kc = self._component_distribution.batch_shape[-1]
        if km is not None and kc is not None and km != kc:
            raise ValueError(
                f"`mixture_distribution component` ({km}) does not"
                " equal `component_distribution.batch_shape[-1]`"
                f" ({kc})"
            )
        self._num_component = km

        event_shape = self._component_distribution.event_shape
        self._event_ndims = len(event_shape)
        super().__init__(
            batch_shape=cdbs, event_shape=event_shape, validate_args=validate_args
        )

    def expand(self, batch_shape, _instance=None):
        batch_shape = torch.Size(batch_shape)
        batch_shape_comp = batch_shape + (self._num_component,)
        new = self._get_checked_instance(MixtureSameFamily, _instance)
        new._component_distribution = self._component_distribution.expand(
            batch_shape_comp
        )
        new._mixture_distribution = self._mixture_distribution.expand(batch_shape)
        new._num_component = self._num_component
        new._event_ndims = self._event_ndims
        event_shape = new._component_distribution.event_shape
        super(MixtureSameFamily, new).__init__(
            batch_shape=batch_shape, event_shape=event_shape, validate_args=False
        )
        new._validate_args = self._validate_args
        return new

    @constraints.dependent_property
    def support(self):
        # FIXME this may have the wrong shape when support contains batched
        # parameters
        return self._component_distribution.support

    @property
    def mixture_distribution(self):
        return self._mixture_distribution

    @property
    def component_distribution(self):
        return self._component_distribution

    @property
    def mean(self):
        probs = self._pad_mixture_dimensions(self.mixture_distribution.probs)
        return torch.sum(
            probs * self.component_distribution.mean, dim=-1 - self._event_ndims
        )  # [B, E]

    @property
    def variance(self):
        # Law of total variance: Var(Y) = E[Var(Y|X)] + Var(E[Y|X])
        probs = self._pad_mixture_dimensions(self.mixture_distribution.probs)
        mean_cond_var = torch.sum(
            probs * self.component_distribution.variance, dim=-1 - self._event_ndims
        )
        var_cond_mean = torch.sum(
            probs * (self.component_distribution.mean - self._pad(self.mean)).pow(2.0),
            dim=-1 - self._event_ndims,
        )
        return mean_cond_var + var_cond_mean

    def cdf(self, x):
        x = self._pad(x)
        cdf_x = self.component_distribution.cdf(x)
        mix_prob = self.mixture_distribution.probs

        return torch.sum(cdf_x * mix_prob, dim=-1)

    def log_prob(self, x):
        if self._validate_args:
            self._validate_sample(x)
        x = self._pad(x)
        log_prob_x = self.component_distribution.log_prob(x)  # [S, B, k]
        log_mix_prob = torch.log_softmax(
            self.mixture_distribution.logits, dim=-1
        )  # [B, k]
        return torch.logsumexp(log_prob_x + log_mix_prob, dim=-1)  # [S, B]

    def sample(self, sample_shape=torch.Size()):
        with torch.no_grad():
            sample_len = len(sample_shape)
            batch_len = len(self.batch_shape)
            gather_dim = sample_len + batch_len
            es = self.event_shape

            # mixture samples [n, B]
            mix_sample = self.mixture_distribution.sample(sample_shape)
            mix_shape = mix_sample.shape

            # component samples [n, B, k, E]
            comp_samples = self.component_distribution.sample(sample_shape)

            # Gather along the k dimension
            mix_sample_r = mix_sample.reshape(
                mix_shape + torch.Size([1] * (len(es) + 1))
            )
            mix_sample_r = mix_sample_r.repeat(
                torch.Size([1] * len(mix_shape)) + torch.Size([1]) + es
            )

            samples = torch.gather(comp_samples, gather_dim, mix_sample_r)
            return samples.squeeze(gather_dim)

    def _pad(self, x):
        return x.unsqueeze(-1 - self._event_ndims)

    def _pad_mixture_dimensions(self, x):
        dist_batch_ndims = len(self.batch_shape)
        cat_batch_ndims = len(self.mixture_distribution.batch_shape)
        pad_ndims = 0 if cat_batch_ndims == 1 else dist_batch_ndims - cat_batch_ndims
        xs = x.shape
        x = x.reshape(
            xs[:-1]
            + torch.Size(pad_ndims * [1])
            + xs[-1:]
            + torch.Size(self._event_ndims * [1])
        )
        return x

    def __repr__(self):
        args_string = (
            f"\n  {self.mixture_distribution},\n  {self.component_distribution}"
        )
        return "MixtureSameFamily" + "(" + args_string + ")"
