import torch
from torch.distributions import constraints
from torch.distributions.distribution import Distribution
from torch.distributions.independent import Independent
from torch.distributions.transforms import ComposeTransform, Transform
from torch.distributions.utils import _sum_rightmost
from typing import Dict


class TransformedDistribution(Distribution):
    r"""
    Extension of the Distribution class, which applies a sequence of Transforms
    to a base distribution.  Let f be the composition of transforms applied::

        X ~ BaseDistribution
        Y = f(X) ~ TransformedDistribution(BaseDistribution, f)
        log p(Y) = log p(X) + log |det (dX/dY)|

    Note that the ``.event_shape`` of a :class:`TransformedDistribution` is the
    maximum shape of its base distribution and its transforms, since transforms
    can introduce correlations among events.

    An example for the usage of :class:`TransformedDistribution` would be::

        # Building a Logistic Distribution
        # X ~ Uniform(0, 1)
        # f = a + b * logit(X)
        # Y ~ f(X) ~ Logistic(a, b)
        base_distribution = Uniform(0, 1)
        transforms = [SigmoidTransform().inv, AffineTransform(loc=a, scale=b)]
        logistic = TransformedDistribution(base_distribution, transforms)

    For more examples, please look at the implementations of
    :class:`~torch.distributions.gumbel.Gumbel`,
    :class:`~torch.distributions.half_cauchy.HalfCauchy`,
    :class:`~torch.distributions.half_normal.HalfNormal`,
    :class:`~torch.distributions.log_normal.LogNormal`,
    :class:`~torch.distributions.pareto.Pareto`,
    :class:`~torch.distributions.weibull.Weibull`,
    :class:`~torch.distributions.relaxed_bernoulli.RelaxedBernoulli` and
    :class:`~torch.distributions.relaxed_categorical.RelaxedOneHotCategorical`
    """
    arg_constraints: Dict[str, constraints.Constraint] = {}

    def __init__(self, base_distribution, transforms, validate_args=None):
        if isinstance(transforms, Transform):
            self.transforms = [transforms, ]
        elif isinstance(transforms, list):
            if not all(isinstance(t, Transform) for t in transforms):
                raise ValueError("transforms must be a Transform or a list of Transforms")
            self.transforms = transforms
        else:
            raise ValueError("transforms must be a Transform or list, but was {}".format(transforms))

        # Reshape base_distribution according to transforms.
        base_shape = base_distribution.batch_shape + base_distribution.event_shape
        base_event_dim = len(base_distribution.event_shape)
        transform = ComposeTransform(self.transforms)
        domain_event_dim = transform.domain.event_dim
        if len(base_shape) < domain_event_dim:
            raise ValueError("base_distribution needs to have shape with size at least {}, but got {}."
                             .format(domain_event_dim, base_shape))
        shape = transform.forward_shape(base_shape)
        expanded_base_shape = transform.inverse_shape(shape)
        if base_shape != expanded_base_shape:
            base_batch_shape = expanded_base_shape[:len(expanded_base_shape) - base_event_dim]
            base_distribution = base_distribution.expand(base_batch_shape)
        reinterpreted_batch_ndims = domain_event_dim - base_event_dim
        if reinterpreted_batch_ndims > 0:
            base_distribution = Independent(base_distribution, reinterpreted_batch_ndims)
        self.base_dist = base_distribution

        # Compute shapes.
        event_dim = transform.codomain.event_dim + max(base_event_dim - domain_event_dim, 0)
        assert len(shape) >= event_dim
        cut = len(shape) - event_dim
        batch_shape = shape[:cut]
        event_shape = shape[cut:]
        super(TransformedDistribution, self).__init__(batch_shape, event_shape, validate_args=validate_args)

    def expand(self, batch_shape, _instance=None):
        new = self._get_checked_instance(TransformedDistribution, _instance)
        batch_shape = torch.Size(batch_shape)
        shape = batch_shape + self.event_shape
        for t in reversed(self.transforms):
            shape = t.inverse_shape(shape)
        base_batch_shape = shape[:len(shape) - len(self.base_dist.event_shape)]
        new.base_dist = self.base_dist.expand(base_batch_shape)
        new.transforms = self.transforms
        super(TransformedDistribution, new).__init__(batch_shape, self.event_shape, validate_args=False)
        new._validate_args = self._validate_args
        return new

    @constraints.dependent_property(is_discrete=False)
    def support(self):
        if not self.transforms:
            return self.base_dist.support
        support = self.transforms[-1].codomain
        if len(self.event_shape) > support.event_dim:
            support = constraints.independent(support, len(self.event_shape) - support.event_dim)
        return support

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

    def sample(self, sample_shape=torch.Size()):
        """
        Generates a sample_shape shaped sample or sample_shape shaped batch of
        samples if the distribution parameters are batched. Samples first from
        base distribution and applies `transform()` for every transform in the
        list.
        """
        with torch.no_grad():
            x = self.base_dist.sample(sample_shape)
            for transform in self.transforms:
                x = transform(x)
            return x

    def rsample(self, sample_shape=torch.Size()):
        """
        Generates a sample_shape shaped reparameterized sample or sample_shape
        shaped batch of reparameterized samples if the distribution parameters
        are batched. Samples first from base distribution and applies
        `transform()` for every transform in the list.
        """
        x = self.base_dist.rsample(sample_shape)
        for transform in self.transforms:
            x = transform(x)
        return x

    def log_prob(self, value):
        """
        Scores the sample by inverting the transform(s) and computing the score
        using the score of the base distribution and the log abs det jacobian.
        """
        event_dim = len(self.event_shape)
        log_prob = 0.0
        y = value
        for transform in reversed(self.transforms):
            x = transform.inv(y)
            event_dim += transform.domain.event_dim - transform.codomain.event_dim
            log_prob = log_prob - _sum_rightmost(transform.log_abs_det_jacobian(x, y),
                                                 event_dim - transform.domain.event_dim)
            y = x

        log_prob = log_prob + _sum_rightmost(self.base_dist.log_prob(y),
                                             event_dim - len(self.base_dist.event_shape))
        return log_prob

    def _monotonize_cdf(self, value):
        """
        This conditionally flips ``value -> 1-value`` to ensure :meth:`cdf` is
        monotone increasing.
        """
        sign = 1
        for transform in self.transforms:
            sign = sign * transform.sign
        if isinstance(sign, int) and sign == 1:
            return value
        return sign * (value - 0.5) + 0.5

    def cdf(self, value):
        """
        Computes the cumulative distribution function by inverting the
        transform(s) and computing the score of the base distribution.
        """
        for transform in self.transforms[::-1]:
            value = transform.inv(value)
        if self._validate_args:
            self.base_dist._validate_sample(value)
        value = self.base_dist.cdf(value)
        value = self._monotonize_cdf(value)
        return value

    def icdf(self, value):
        """
        Computes the inverse cumulative distribution function using
        transform(s) and computing the score of the base distribution.
        """
        value = self._monotonize_cdf(value)
        if self._validate_args:
            self.base_dist._validate_sample(value)
        value = self.base_dist.icdf(value)
        for transform in self.transforms:
            value = transform(value)
        return value