ott.geometry.costs.SqPNorm

Contents

ott.geometry.costs.SqPNorm#

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

Squared p-norm 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, \(\ge 1\).

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)

Barycentric operator.

h(z)

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

h_legendre(z)

Legendre transform of h().

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