TML (version 2.3.0)

trop.Volume: 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)

Value

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

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

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

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)