ott.geometry.costs.PNormP

class ott.geometry.costs.PNormP(p)

\(p\)-norm to the power \(p\) and divided by \(p\).

Uses custom implementation of norm to avoid NaN values when differentiating the norm of \(x-x\).

Parameters:

p (float) – Power of the p-norm in \([1, +\infty)\). Note that h_legendre() is not defined for p = 1.

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() when it is convex.
h_transform(f[, ridge, solver])	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.