import torch
import numpy as np


class AbstractDistribution:
    def sample(self):
        raise NotImplementedError()

    def mode(self):
        raise NotImplementedError()


class DiracDistribution(AbstractDistribution):
    def __init__(self, value):
        self.value = value

    def sample(self):
        return self.value

    def mode(self):
        return self.value


class DiagonalGaussianDistribution(object):
    def __init__(self, parameters, deterministic=False):
        """
        parameters: input is expected to be a 2D tensor, where the first
                    half of the last dimension are the means and the second
                    half are the log-variances.
        deterministic: if set to True, would mean that there is no randomness in the distribution
                       (i.e., variance and standard deviation are set to zero).
        mathematical:
            self.mean = µ
            self.std = σ
            self.var = σ^2
            self.logvar = log(σ^2) = 2log(σ)
                The logarithm of the variance (self.logvar) is also often used in formulas
                in statistics. For example, the log-likelihood of a Gaussian distribution
                involves the log of the variance. Therefore, working directly with the log
                -variance can make the formulas simpler and more numerically stable.
        """
        self.parameters = parameters
        self.mean, self.logvar = torch.chunk(parameters, 2, dim=1)
        self.logvar = torch.clamp(self.logvar, -30.0, 20.0)
        self.deterministic = deterministic
        self.std = torch.exp(0.5 * self.logvar)
        self.var = torch.exp(self.logvar)
        if self.deterministic:
            self.var = self.std = torch.zeros_like(self.mean).to(device=self.parameters.device)

    def sample(self):
        """
        Reparameterization:
        if Z is a standard normal random variable (i.e., Gaussian distributed
        with mean 0 and standard deviation 1), X = μ + σZ is a normal random
        variable with mean μ and standard deviation σ.
        """
        x = self.mean + self.std * torch.randn(self.mean.shape).to(device=self.parameters.device)
        return x

    def kl(self, other=None):
        """
        This function is to compute the KL-divergence of the current
        Gaussian distribution with another one. If other is None, then
        compute the KL-divergence with a standard distribution.
        $ KL(P||Q) = log(σ_2 / σ_1) + \frac{σ_1^2 + (μ1 - μ2)^2}{2σ_2^2} - 0.5 $
        """
        if self.deterministic:
            return torch.Tensor([0.])
        else:
            if other is None:
                return 0.5 * torch.sum(torch.pow(self.mean, 2)
                                       + self.var - 1.0 - self.logvar,
                                       dim=[1, 2, 3])
            else:
                return 0.5 * torch.sum(
                    torch.pow(self.mean - other.mean, 2) / other.var
                    + self.var / other.var - 1.0 - self.logvar + other.logvar,
                    dim=[1, 2, 3])

    def nll(self, sample, dims=[1, 2, 3]):
        """
        The negative log likelihood (NLL) of observing a sample x from a normal
        distribution with mean μ and variance σ^2 is given by:
        NLL = 0.5 * log(2πσ^2) + (1 / 2σ^2) * (x - μ)^2
        """
        if self.deterministic:
            return torch.Tensor([0.])
        logtwopi = np.log(2.0 * np.pi)
        return 0.5 * torch.sum(
            logtwopi + self.logvar + torch.pow(sample - self.mean, 2) / self.var,
            dim=dims)

    def mode(self):
        return self.mean


def normal_kl(mean1, logvar1, mean2, logvar2):
    """
    source: https://github.com/openai/guided-diffusion/blob/27c20a8fab9cb472df5d6bdd6c8d11c8f430b924/guided_diffusion/losses.py#L12
    Compute the KL divergence between two Gaussians.
    Shapes are automatically broadcasted, so batches can be compared to
    scalars, among other use cases.
    """
    tensor = None
    for obj in (mean1, logvar1, mean2, logvar2):
        if isinstance(obj, torch.Tensor):
            tensor = obj
            break
    assert tensor is not None, "at least one argument must be a Tensor"

    # Force variances to be Tensors. Broadcasting helps convert scalars to
    # Tensors, but it does not work for torch.exp().
    logvar1, logvar2 = [
        x if isinstance(x, torch.Tensor) else torch.tensor(x).to(tensor)
        for x in (logvar1, logvar2)
    ]

    return 0.5 * (
        -1.0
        + logvar2
        - logvar1
        + torch.exp(logvar1 - logvar2)
        + ((mean1 - mean2) ** 2) * torch.exp(-logvar2)
    )