# sources: 
# https://www.kaggle.com/code/ibtesama/gan-in-pytorch-with-fid/notebook
# https://github.com/mseitzer/pytorch-fid/blob/master/src/pytorch_fid/fid_score.py

import numpy as np
from scipy import linalg
from torch.nn.functional import adaptive_avg_pool2d


def calculate_activation_statistics(images, model, batch_size=128, dims=2048):
    model.eval()
    act = np.empty((len(images), dims))

    batch = images
    pred = model(batch)[0]

    # If model output is not scalar, apply global spatial average pooling.
    # This happens if you choose a dimensionality not equal 2048.
    if pred.size(2) != 1 or pred.size(3) != 1:
        pred = adaptive_avg_pool2d(pred, output_size=(1, 1))

    act = pred.cpu().data.numpy().reshape(pred.size(0), -1)
    
    mu = np.mean(act, axis=0)
    sigma = np.cov(act, rowvar=False)
    return mu, sigma


def calculate_frechet_distance(mu1, sigma1, mu2, sigma2, eps=1e-6):
    """Numpy implementation of the Frechet Distance.
    The Frechet distance between two multivariate Gaussians X_1 ~ N(mu_1, C_1)
    and X_2 ~ N(mu_2, C_2) is
            d^2 = ||mu_1 - mu_2||^2 + Tr(C_1 + C_2 - 2*sqrt(C_1*C_2)).
    """

    mu1 = np.atleast_1d(mu1)
    mu2 = np.atleast_1d(mu2)

    sigma1 = np.atleast_2d(sigma1)
    sigma2 = np.atleast_2d(sigma2)

    assert mu1.shape == mu2.shape, \
        'Training and test mean vectors have different lengths'
    assert sigma1.shape == sigma2.shape, \
        'Training and test covariances have different dimensions'

    diff = mu1 - mu2

    
    covmean, _ = linalg.sqrtm(sigma1.dot(sigma2), disp=False)
    if not np.isfinite(covmean).all():
        msg = ('fid calculation produces singular product; '
               'adding %s to diagonal of cov estimates') % eps
        print(msg)
        offset = np.eye(sigma1.shape[0]) * eps
        covmean = linalg.sqrtm((sigma1 + offset).dot(sigma2 + offset))

    
    if np.iscomplexobj(covmean):
        if not np.allclose(np.diagonal(covmean).imag, 0, atol=1e-3):
            m = np.max(np.abs(covmean.imag))
            raise ValueError('Imaginary component {}'.format(m))
        covmean = covmean.real

    tr_covmean = np.trace(covmean)

    return (diff.dot(diff) + np.trace(sigma1) +
            np.trace(sigma2) - 2 * tr_covmean)


def calculate_fretchet(images_real, images_fake, model):
    """Calculate the fretched distance."""
     
    # calculate statistics (mean + std)
    mu_1, std_1 = calculate_activation_statistics(images_real, model)
    mu_2, std_2 = calculate_activation_statistics(images_fake, model)
    
    # compute distance
    fid_value = calculate_frechet_distance(mu_1, std_1, mu_2, std_2)
    return fid_value