trop.Volume: Estimate the volume of a tropical polytope

In TML: Tropical Geometry Tools for Machine Learning

Estimate the volume of a tropical polytope

Description

This function uses tropical HAR with a uniform target distribution to estimate the volume of a tropical polytope

Usage

trop.Volume(B, P, x0, s, I, r)

Arguments

B	matrix of points defining a minimum enclosing ball for a polytope P; rows are the points
P	matrix of points defining a tropical polytope; rows are the points
x0	initial point used for the HAR sampler
s	number of points to sample from the minimum enclosing ball
I	number of iterations for the HAR sampler
r	radius of the minimum enclosing tropical ball

Value

list containing ratio of points falling in P; volume of the tropical ball; volume estimate of P

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

P <-matrix(c(0,0,0,0,3,1,0,2,5),3,3,TRUE)
BR<-min_enc.ball(P)
B<-trop.bal.vert(BR[[1]],BR[[2]])
x0<-c(0,1.5,.4)
S<-200
I<-50
R<-BR[[2]]
trop.Volume(B,P,x0,S,I,R)

TML documentation built on Sept. 11, 2024, 6:19 p.m.