ott.geometry.costs.SqPNorm#

class ott.geometry.costs.SqPNorm(p)[source]#

Squared p-norm of the difference of two vectors.

For details on the derivation of the Legendre transform of the norm, see e.g. the reference [Boyd et al., 2004], p.93/94.

Parameters

p (float) – Power of the p-norm.

Methods

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.

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 \(x-y\).

Attributes

norm