ott.geometry.distrib_costs.UnivariateWasserstein

class ott.geometry.distrib_costs.UnivariateWasserstein(solve_fn, ground_cost=None)

1D Wasserstein cost for two 1D distributions.

This ground cost between considers vectors as a family of values. The Wasserstein distance between them is the 1D OT cost, using a user-defined ground cost.

Parameters:

• solve_fn (Callable[[LinearProblem], UnivariateOutput]) – 1D optimal transport solver, e.g., uniform_distance().

• ground_cost (Optional[TICost]) – Cost used to compute the 1D optimal transport between vectors. Should be a translation-invariant (TI) cost for correctness. If None, defaults to SqEuclidean.

Methods

all_pairs(x, y)	Compute matrix of all pairwise costs, including the norms.
barycenter(weights, xs)	Barycentric operator.
twist_operator(vec, dual_vec, variable)	Twist inverse operator of the cost function.