# The index of the vertex region in a middle interval that contains a given point Returns the index of the vertex whose region contains point `p` in the interval `int`$=(a,b)=$(vertex 1,vertex 2) with (parameterized) center $M_c$ associated with the centrality parameter $c \in (0,1)$; vertices of interval are labeled as 1 and 2 according to their order in the interval `int`. If the point, `p`, is not inside `int`, then the function yields `NA` as output. The corresponding vertex region is the interval $(a,b)$ as $(a,M_c)$ and $(M_c,b)$ where $M_c=a+c(b-a)$. 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.mid.int(p, int, c = 0.5) ``` ## Arguments - `p`: A 1D point. The vertex region `p` resides is to be found. - `int`: A `vector` of two real numbers representing an interval. - `c`: A positive real number in $(0,1)$ parameterizing the center inside `int`$=(a,b)$ with the default `c=.5`. For the interval, `int`$=(a,b)$, the parameterized center is $M_c=a+c(b-a)$. ## Returns A `list` with two elements - **rv**: Index of the vertex in the interval `int` 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 c<-.4 a<-0; b<-10; int = c(a,b) Mc<-centerMc(int,c) rel.vert.mid.int(6,int,c) n<-20 #try also n<-40 xr<-range(a,b,Mc) xf<-(int[2]-int[1])*.5 Xp<-runif(n,a,b) Rv<-vector() for (i in 1:n) Rv<-c(Rv,rel.vert.mid.int(Xp[i],int,c)$rv) Rv jit<-.1 yjit<-runif(n,-jit,jit) Xlim<-range(a,b,Xp) xd<-Xlim[2]-Xlim[1] plot(cbind(Mc,0),main="vertex region indices for the points", xlab=" ", ylab=" ", xlim=Xlim+xd*c(-.05,.05),ylim=3*range(yjit),pch=".",cex=3) abline(h=0) points(Xp,yjit) abline(v=c(a,b,Mc),lty = 2,col=c(1,1,2)) text(Xp,yjit,labels=factor(Rv)) text(cbind(c(a,b,Mc),.02),c("rv=1","rv=2","Mc")) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `rel.vert.end.int` ## Author(s) Elvan Ceyhan

rel.vert.mid.int function