This module provides functions for linearization of the quadratic Wasserstein distance W₂ (see for example https://en.wikipedia.org/wiki/Wasserstein_metric) between two nonnegative distributions of equal mass defined on the unit square [0,1]² ⊂ ℝ². In particular, this module provides a code to approximate the negative weighted homogeneous Sobolev norm via a method that involves the Witten Laplacian H, which is a Schrödinger operator of the form
H = -Δ + V,
where V is a potential function. The primary numerical task for this local approximation of W₂ is the numerical solution to the elliptic equation
H ψ = u
For a detailed description of the numerical algorithm used in this module as well as the corresponding analysis, see [arXiv].