import torch
from torch.distributions import Distribution, Normal
import mbrl.torch_modules.utils as ptu


class TanhNormal(Distribution):
    """
    Represent distribution of X where
        X ~ tanh(Z)
        Z ~ N(mean, std)

    Note: this is not very numerically stable.
    """
    def __init__(self, normal_mean, normal_std, epsilon=1e-6):
        """
        :param normal_mean: Mean of the normal distribution
        :param normal_std: Std of the normal distribution
        :param epsilon: Numerical stability epsilon when computing log-prob.
        """
        self.normal_mean = normal_mean
        self.normal_std = normal_std
        self.normal = Normal(normal_mean, normal_std)
        self.epsilon = epsilon

    def log_prob(self, value, pre_tanh_value=None):
        """

        :param value: some value, x
        :param pre_tanh_value: arctanh(x)
        :return:
        """
        if pre_tanh_value is None:
            pre_tanh_value = torch.log(
                (1+value) / (1-value)
            ) / 2
        return self.normal.log_prob(pre_tanh_value) - torch.log(
            1 - value * value + self.epsilon
        )

    def sample(self, shape=(), return_pretanh_value=False):
        """
        Gradients will and should *not* pass through this operation.

        See https://github.com/pytorch/pytorch/issues/4620 for discussion.
        """
        z = self.normal.sample(shape).detach()

        if return_pretanh_value:
            return torch.tanh(z), z
        else:
            return torch.tanh(z)

    def rsample(self, shape=(), return_pretanh_value=False):
        """
        Sampling in the reparameterization case.
        """
        z = (
            self.normal_mean +
            self.normal_std *
            Normal(
                ptu.zeros(self.normal_mean.size()),
                ptu.ones(self.normal_std.size())
            ).sample(shape)
        )
        z.requires_grad_()

        if return_pretanh_value:
            return torch.tanh(z), z
        else:
            return torch.tanh(z)
