#!/usr/bin/env python3
"""Calculates the Frechet Distance (FD) between two samples.

Code apapted from https://github.com/bioinf-jku/TTUR to use PyTorch instead
of Tensorflow

Copyright 2018 Institute of Bioinformatics, JKU Linz

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

   http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
"""
import numpy as np
import torch
from scipy import linalg

def sample_frechet_distance(sample1, sample2, eps=1e-6,
        return_components=False):
    '''
    Both samples should be numpy arrays.
    Returns the Frechet distance.
    '''
    (mu1, sigma1), (mu2, sigma2) = [calculate_activation_statistics(s)
            for s in [sample1, sample2]]
    return calculate_frechet_distance(mu1, sigma1, mu2, sigma2, eps=eps,
            return_components=return_components)

def calculate_frechet_distance(mu1, sigma1, mu2, sigma2, eps=1e-6,
        return_components=False):
    """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)).

    Stable version by Dougal J. Sutherland.

    Params:
    -- mu1   : Numpy array containing the activations of a layer of the
               inception net (like returned by the function 'get_predictions')
               for generated samples.
    -- mu2   : The sample mean over activations, precalculated on an
               representative data set.
    -- sigma1: The covariance matrix over activations for generated samples.
    -- sigma2: The covariance matrix over activations, precalculated on an
               representative data set.

    Returns:
    --   : The Frechet Distance.
    """

    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

    # Product might be almost singular
    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))

    # Numerical error might give slight imaginary component
    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)

    meandiff = diff.dot(diff)
    covdiff = np.trace(sigma1) + np.trace(sigma2) - 2 * tr_covmean
    if return_components:
        return (meandiff + covdiff, meandiff, covdiff)
    else:
        return meandiff + covdiff


def calculate_activation_statistics(act):
    """Calculation of the statistics used by the FID.
    Params:
    -- files       : List of image files paths
    -- model       : Instance of inception model
    -- batch_size  : The images numpy array is split into batches with
                     batch size batch_size. A reasonable batch size
                     depends on the hardware.
    -- dims        : Dimensionality of features returned by Inception
    -- cuda        : If set to True, use GPU
    -- verbose     : If set to True and parameter out_step is given, the
                     number of calculated batches is reported.
    Returns:
    -- mu    : The mean over samples of the activations of the pool_3 layer of
               the inception model.
    -- sigma : The covariance matrix of the activations of the pool_3 layer of
               the inception model.
    """
    mu = np.mean(act, axis=0)
    sigma = np.cov(act, rowvar=False)
    return mu, sigma