# The indicator for a point being a dominating point for Central Similarity Proximity Catch Digraphs (CS-PCDs) for an interval Returns $I($`p` is a dominating point of CS-PCD$)$ where the vertices of the CS-PCD are the 1D data set `Xp`). CS proximity region is defined with respect to the interval `int` with an expansion parameter, $t>0$, and a centrality parameter, $c \in (0,1)$, so arcs may exist for `Xp` points inside the interval `int`$=(a,b)$. Vertex regions are based on the center associated with the centrality parameter $c \in (0,1)$. `rv` is the index of the vertex region `p` resides, with default=`NULL`. `ch.data.pnt` is for checking whether point `p` is a data point in `Xp` or not (default is `FALSE`), so by default this function checks whether the point `p` would be a dominating point if it actually were in the data set. ```r Idom.num1CSint(p, Xp, int, t, c = 0.5, rv = NULL, ch.data.pnt = FALSE) ``` ## Arguments - `p`: A 1D point that is to be tested for being a dominating point or not of the CS-PCD. - `Xp`: A set of 1D points which constitutes the vertices of the CS-PCD. - `int`: A `vector` of two real numbers representing an interval. - `t`: A positive real number which serves as the expansion parameter in CS proximity region. - `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 $M_c=a+c(b-a)$. - `rv`: Index of the vertex region in which the point resides, either `1,2` or `NULL` (default is `NULL`). - `ch.data.pnt`: A logical argument for checking whether point `p` is a data point in `Xp` or not (default is `FALSE`). ## Returns $I($`p` is a dominating point of CS-PCD$)$ where the vertices of the CS-PCD are the 1D data set `Xp`), that is, returns 1 if `p` is a dominating point, returns 0 otherwise ## Examples ```r t<-2 c<-.4 a<-0; b<-10; int<-c(a,b) Mc<-centerMc(int,c) n<-10 set.seed(1) Xp<-runif(n,a,b) Idom.num1CSint(Xp[5],Xp,int,t,c) Idom.num1CSint(2,Xp,int,t,c,ch.data.pnt = FALSE) #gives an error if ch.data.pnt = TRUE since p is not a data point in Xp gam.vec<-vector() for (i in 1:n) {gam.vec<-c(gam.vec,Idom.num1CSint(Xp[i],Xp,int,t,c))} ind.gam1<-which(gam.vec==1) ind.gam1 domset<-Xp[ind.gam1] if (length(ind.gam1)==0) {domset<-NA} #or try Rv<-rel.vert.mid.int(Xp[5],int,c)$rv Idom.num1CSint(Xp[5],Xp,int,t,c,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,Mc),col=c(1,1,2),lty=2) points(cbind(Xp,0)) points(cbind(domset,0),pch=4,col=2) text(cbind(c(a,b,Mc),-0.1),c("a","b","Mc")) Idom.num1CSint(Xp[5],Xp,int,t,c) n<-10 Xp2<-runif(n,a+b,b+10) Idom.num1CSint(5,Xp2,int,t,c) ``` ## See Also `Idom.num1PEint` ## Author(s) Elvan Ceyhan

Idom.num1CSint function