ott.geometry.costs.PNormP#
- class ott.geometry.costs.PNormP(p)[source]#
\(p\)-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 thath_legendre()
is not defined forp = 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.
Get an optimal transport map for a concave function \(g\).
twist_operator
(vec, dual_vec, variable)Twist inverse operator of the cost function.