trop.bal.vert {TML}

Calculate the minimum or entire generating vertex set of a tropical ball using a max- or min-plus algebra

Description

This function calculates the coordinates of the minimum or entire vertex set of a tropical ball in terms of either a max- or min-plus algebra for a given a center point

Usage

trop.bal.vert(x, d, tadd = max)

trop.bal.all_vert(x, d)

Arguments

x

matrix where each row is a point defining a tropical polytope

d

radius of the tropical ball in terms of tropical distance

tadd

function; max indicates max-plus addition, min indicates min-plus addition, 'all' indicates all vertices. Defaults to 'max'

Value

matrix of normalized tropical points defining the tropical ball. Rows are the points

Author(s)

David Barnhill [e-mail]

References

Barnhill, David, Ruriko Yoshida and Keiji Miura (2023). Maximum Inscribed and Minimum Enclosing Tropical Balls of Tropical Polytopes and Applications to Volume Estimation and Uniform Sampling.

Examples

x <-c(0,3,7,5)
d <- 2
trop.bal.vert(x,d)
trop.bal.vert(x,d,tadd=min)
trop.bal.all_vert(x,d)