Compile and run VolEsti. Use the R extension to visualize sampling in a polytope.

Here are the libraries needed

options(tinytex.verbose = TRUE)
library(ggplot2)
library(volesti)
## Loading required package: Rcpp

keep a polytope as a variable after reading a .ine file

options(tinytex.verbose = TRUE)
polytope = file_to_polytope("/home/haris/volume_approximation/R-proj/inst/extdata/cross_10.ine")

random sampling with different algorithms

options(tinytex.verbose = TRUE)
points_cdhr =  sample_points(P = polytope, n = 5000, distribution = list("density" = "uniform"),  random_walk = list("walk"="CDHR"))
points_rdhr =  sample_points(P = polytope, n = 5000, distribution = list("density" = "uniform"),  random_walk = list("walk"="RDHR"))
points_biw =  sample_points(P = polytope, n = 5000, distribution = list("density" = "uniform"),  random_walk = list("walk"="BiW"))
points_baw =  sample_points(P = polytope, n = 5000, distribution = list("density" = "uniform"),  random_walk = list("walk"="BaW"))

keep sample points

options(tinytex.verbose = TRUE)
BaW = data.frame(x=points_baw[1,], y=points_baw[2,])
BiW = data.frame(x=points_biw[1,], y=points_biw[2,])
CDHR = data.frame(x=points_cdhr[1,], y=points_cdhr[2,])
RDHR = data.frame(x=points_rdhr[1,], y=points_rdhr[2,])

bind all the points in a dataframe

options(tinytex.verbose = TRUE)
walks = rbind(BaW,BiW,CDHR,RDHR)

add a column in the dataframe to tag the points of each algorithm

walks$random_walk = c(rep("BaW",5000),rep("BiW",5000),rep("CDHR",5000),rep("RDHR",5000))

plot it

ggplot(walks, aes(x=x, y=y, group=random_walk,col=random_walk)) + 
  geom_point() + labs(title = "uniform sampling on cross_10.ine file / H-polytope")

more sampling, more plots

P = gen_cube(2, 'H')
p=sample_points(P, n=2000, random_walk = list("walk" = "BiW", "walk_length" = 1))
r = t(p)
q = as.data.frame(r)
names(q)[1]='x'
names(q)[2]='y'
ggplot(q, aes(x=x,y=y)) +
       geom_point()

Get sample points from the inside of polytope.

P = gen_rand_hpoly(2,17, seed=1917)
p=sample_points(P, n=2000, random_walk = list("walk" = "RDHR", "walk_length" = 1))
r = t(p)
q1 = as.data.frame(r)
names(q1)[1]='x'
names(q1)[2]='y'
ggplot(q1, aes(x=x,y=y)) +
       geom_point()

Get boundary points from the same polytope.

p=sample_points(P, n=2000, random_walk = list("walk" = "BRDHR", "walk_length" = 1))
r = t(p)
q2 = as.data.frame(r)
names(q2)[1]='x'
names(q2)[2]='y'
ggplot(q2, aes(x=x,y=y)) +
       geom_point()

and together..

final_points=rbind(q1,q2)
final_points$random_walk = c(rep("RDHR",2000), rep("BRDHR",2000))

ggplot(final_points, aes(x=x, y=y, group=random_walk,col=random_walk)) + 
  geom_point() + labs(title = "in and out random walks")