ott.geometry.costs.PNormP

class ott.geometry.costs.PNormP(p)

p-norm to the power p (and divided by p) of the difference of two vectors.

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.
all_pairs_pairwise(x, y)	Compute matrix of all pairwise costs, excluding 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.
pairwise(x, y)	Compute cost as evaluation of h() on \(x-y\).
twist_operator(vec, dual_vec, variable)	Twist inverse operator of the cost function.

Attributes

norm