# The index of the vertex region in an end-interval that contains a given point Returns the index of the vertex in the interval, `int`, whose end interval contains the 1D point `p`, that is, it finds the index of the vertex for the point, `p`, outside the interval `int`$=(a,b)=$(vertex 1,vertex 2); vertices of interval are labeled as 1 and 2 according to their order in the interval. If the point, `p`, is inside `int`, then the function yields `NA` as output. The corresponding vertex region is an interval as $(-\infty,a)$ or $(b,\infty)$ for the interval $(a,b)$. Then if $pb$, then `rv=2`. Unlike `rel.vert.mid.int`, centrality parameter (i.e., center of the interval is not relevant for `rel.vert.end.int`.) See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:metrika-2012,ceyhan:revstat-2016;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r rel.vert.end.int(p, int) ``` ## Arguments - `p`: A 1D point whose end interval region is provided by the function. - `int`: A `vector` of two real numbers representing an interval. ## Returns A `list` with two elements - **rv**: Index of the end vertex whose region contains point, `p`. - **int**: The vertices of the interval as a `vector` where position of the vertex corresponds to the vertex index as `int=(rv=1,rv=2)`. ## Examples ```r a<-0; b<-10; int<-c(a,b) rel.vert.end.int(-6,int) rel.vert.end.int(16,int) n<-10 xf<-(int[2]-int[1])*.5 XpL<-runif(n,a-xf,a) XpR<-runif(n,b,b+xf) Xp<-c(XpL,XpR) rel.vert.end.int(Xp[1],int) Rv<-vector() for (i in 1:length(Xp)) Rv<-c(Rv,rel.vert.end.int(Xp[i],int)$rv) Rv Xlim<-range(a,b,Xp) xd<-Xlim[2]-Xlim[1] plot(cbind(a,0),xlab="",pch=".",xlim=Xlim+xd*c(-.05,.05)) abline(h=0) abline(v=c(a,b),col=1,lty = 2) points(cbind(Xp,0)) text(cbind(Xp,0.1),labels=factor(Rv)) text(cbind(c(a,b),-0.1),c("rv=1","rv=2")) jit<-.1 yjit<-runif(length(Xp),-jit,jit) Xlim<-range(a,b,Xp) xd<-Xlim[2]-Xlim[1] plot(cbind(a,0), main="vertex region indices for the points\n in the end intervals", xlab=" ", ylab=" ",pch=".",xlim=Xlim+xd*c(-.05,.05),ylim=3*range(yjit)) points(Xp, yjit,xlim=Xlim+xd*c(-.05,.05),pch=".",cex=3) abline(h=0) abline(v=c(a,b),lty = 2) text(Xp,yjit,labels=factor(Rv)) text(cbind(c(a,b),-.01),c("rv=1","rv=2")) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `rel.vert.mid.int` ## Author(s) Elvan Ceyhan

rel.vert.end.int function