ott.geometry.costs.RegTICost

class ott.geometry.costs.RegTICost(regularizer, lam=1.0, *, rho=1.0)

Regularized translation-invariant cost.

\[\frac{\rho}{2}\|\cdot\|_2^2 + \lambda \text{regularizer}\left(\cdot\right)\]

Parameters:

• regularizer (ProximalOperator) – Regularization function.

• lam (float) – Strength of the regularization.

• rho (float) – Strength of the quadratic part.

Methods

all_pairs(x, y)	Compute matrix of all pairwise costs, including the norms.
barycenter(weights, xs)	Output barycenter of vectors.
h(z)	TI function acting on difference of \(x-y\) to output cost.
h_legendre(z)	Legendre transform of h().
h_transform(f)	Compute the h-transform of a concave function.
transport_map(g)	Get an optimal transport map for a concave function \(g\).
twist_operator(vec, dual_vec, variable)	Twist inverse operator of the cost function.

Attributes

lam	Strength of the regularization.
rho	Strength of the quadratic part \(\frac{\rho}{2}\|\cdot\|_2^2\).