# ott.geometry.costs.TICost#

class ott.geometry.costs.TICost[source]#

A class for translation invariant (TI) costs.

Such costs are defined using a function $$h$$, mapping vectors to real-values, to be used as:

$c(x,y) = h(z), z := x-y.$

If that cost function is used to form an Entropic map using the theorem, then the user should ensure $$h$$ is strictly convex, as well as provide the Legendre transform of $$h$$, whose gradient is necessarily the inverse of the gradient of $$h$$.

Methods

 all_pairs(x, y) Compute matrix of all costs (including norms) for vectors in x / y. all_pairs_pairwise(x, y) Compute matrix of all pairwise-costs (no norms) for vectors in x / y. barycenter(weights, xs) Barycentric operator. h(z) TI function acting on difference of $$x-y$$ to output cost. h_legendre(z) Legendre transform of h() when it is convex. pairwise(x, y) Compute cost as evaluation of h() on $$x-y$$.

Attributes