deeplearning/modulus/modulus-core-v040/_modules/modulus/metrics/general/wasserstein.html

Core v0.4.0

Source code for modulus.metrics.general.wasserstein

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import torch

Tensor = torch.Tensor


[docs]def wasserstein(bin_edges: Tensor, cdf_x: Tensor, cdf_y: Tensor) -> Tensor: """1-Wasserstein distance between two discrete CDF functions This norm is typically used to compare two different forecast ensembles (for X and Y). Creates a map of distance and does not accumulate over lat/lon regions. Computes .. math:: W(F_X, F_Y) = int[ |F_X(x) - F_Y(x)| ] dx where F_X is the empirical cdf of X and F_Y is the empirical cdf of Y. Parameters ---------- bin_edges : Tensor Tensor containing bin edges. The leading dimension must represent the N+1 bin edges. cdf_x : Tensor Tensor containing a CDF one, defined over bins. The non-zeroth dimensions of bins and cdf must be compatible. cdf_y : Tensor Tensor containing a CDF two, defined over bins. Must be compatible with cdf_x in terms of bins and shape. Returns ------- Tensor The 1-Wasserstein distance between cdf_x and cdf_y """ return torch.sum( torch.abs(cdf_x - cdf_y) * (bin_edges[1, ...] - bin_edges[0, ...]), dim=0 )
© Copyright 2023, NVIDIA Modulus Team. Last updated on Jan 25, 2024.