# The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - end-interval case Returns $I(p_2$ in $N_{CS}(p_1,t))$ for points $p_1$ and $p_2$, that is, returns 1 if $p_2$ is in $N_{CS}(p_1,t)$, returns 0 otherwise, where $N_{CS}(x,t)$ is the CS proximity region for point $x$ with expansion parameter $t>0$ for the region outside the interval $(a,b)$. `rv` is the index of the end vertex region $p_1$ resides, with default=`NULL`, and `rv=1` for left end-interval and `rv=2` for the right end-interval. If $p_1$ and $p_2$ are distinct and either of them are inside interval `int`, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops). See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:revstat-2016;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r IarcCSend.int(p1, p2, int, t, rv = NULL) ``` ## Arguments - `p1`: A 1D point for which the CS proximity region is constructed. - `p2`: A 1D point to check whether it is inside the proximity region or not. - `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. - `rv`: Index of the end-interval containing the point, either `1,2` or `NULL` (default=`NULL`). ## Returns $I(p_2$ in $N_{CS}(p_1,t))$ for points $p_1$ and $p_2$, that is, returns 1 if $p_2$ is in $N_{CS}(p_1,t)$ (i.e., if there is an arc from $p_1$ to $p_2$), returns 0 otherwise ## Examples ```r a<-0; b<-10; int<-c(a,b) t<-2 IarcCSend.int(15,17,int,t) IarcCSend.int(15,15,int,t) IarcCSend.int(1.5,17,int,t) IarcCSend.int(1.5,1.5,int,t) IarcCSend.int(-15,17,int,t) IarcCSend.int(-15,-17,int,t) a<-0; b<-10; int<-c(a,b) t<-.5 IarcCSend.int(15,17,int,t) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `IarcCSmid.int`, `IarcPEmid.int`, and `IarcPEend.int` ## Author(s) Elvan Ceyhan

IarcCSend.int function