torchaudio.functional.frechet_distance¶
- torchaudio.functional.frechet_distance(mu_x, sigma_x, mu_y, sigma_y)[source]¶
Computes the Fréchet distance between two multivariate normal distributions [Dowson and Landau, 1982].
Concretely, for multivariate Gaussians \(X(\mu_X, \Sigma_X)\) and \(Y(\mu_Y, \Sigma_Y)\), the function computes and returns \(F\) as
\[F(X, Y) = || \mu_X - \mu_Y ||_2^2 + \text{Tr}\left( \Sigma_X + \Sigma_Y - 2 \sqrt{\Sigma_X \Sigma_Y} \right) \]- Parameters:
mu_x (torch.Tensor) – mean \(\mu_X\) of multivariate Gaussian \(X\), with shape (N,).
sigma_x (torch.Tensor) – covariance matrix \(\Sigma_X\) of \(X\), with shape (N, N).
mu_y (torch.Tensor) – mean \(\mu_Y\) of multivariate Gaussian \(Y\), with shape (N,).
sigma_y (torch.Tensor) – covariance matrix \(\Sigma_Y\) of \(Y\), with shape (N, N).
- Returns:
the Fréchet distance between \(X\) and \(Y\).
- Return type:
