ott.geometry.costs.RegTICost

Contents

ott.geometry.costs.RegTICost#

class ott.geometry.costs.RegTICost(regularizer, lam=1.0, *, rho=1.0)[source]#

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 \(\frac{\rho}{2}\|\cdot\|_2^2\).