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 [Brenier, 1991] 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 \(h\).


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.


TI function acting on difference of \(x-y\) to output cost.


Legendre transform of h() when it is convex.

pairwise(x, y)

Compute cost as evaluation of h() on \(x-y\).