rel.vert.mid.int: The index of the vertex region in a middle interval that...

In pcds: Proximity Catch Digraphs and Their Applications

The index of the vertex region in a middle interval that contains a given point

Description

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 (\insertCiteceyhan:metrika-2012,ceyhan:revstat-2016;textualpcds).

Usage

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).

Value

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).

Author(s)

Elvan Ceyhan

References

\insertAllCited

See Also

rel.vert.end.int

Examples

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"))

pcds documentation built on May 29, 2024, 9:36 a.m.