TML (version 2.3.0)

trop.bal.vert: 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)

Value

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

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'

Author

David Barnhill

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)