library("TDA")


XX1 = circleUnif(600)
XX2 = circleUnif(1000, r=1.5) +2.5
noise=cbind(runif(80, -2,5),runif(80, -2,5))
X=rbind(XX1,XX2, noise)
Xlim=c(-2,5)
Ylim=c(-2,5)
by=0.2

parametersKDE=seq(0.1,0.6,by=0.05)
B=50 # number of bootstrap iterations. Should be large.
alpha=0.1 # level of the confidence bands

maxKDE=maxPersistence(kde, parametersKDE, X, lim=cbind(Xlim, Ylim), by=by, sublevel=F, B=B, alpha=alpha,parallel=TRUE, bandFUN="bootstrapBand")
print(summary(maxKDE))

par(mfrow=c(1,2), mai=c(0.8,0.8,0.35,0.3))
plot(X, pch=16, cex=0.5, main="Two Circles + Noise", xlab="", ylab="")
plot(maxKDE, main="Max Persistence (KDE)")