# Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) for 1D data - multiple interval case Returns the incidence matrix for the CS-PCD for a given 1D numerical data set, `Xp`, as the vertices of the digraph and `Yp` determines the end points of the intervals (in the multi-interval case). If there are duplicates of `Yp` points, only one point is retained for each duplicate value, and a warning message is printed. Loops are allowed, so the diagonal entries are all equal to 1. CS proximity region is constructed with an expansion parameter $t>0$ and a centrality parameter $c \in (0,1)$. 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 inci.matCS1D(Xp, Yp, t, c = 0.5) ``` ## Arguments - `Xp`: a set of 1D points which constitutes the vertices of the digraph. - `Yp`: a set of 1D points which constitutes the end points of the intervals that partition the real line. - `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 middle intervals with the default `c=.5`. For the interval, `int`$=(a,b)$, the parameterized center is $M_c=a+c(b-a)$. ## Returns Incidence matrix for the CS-PCD with vertices being 1D data set, `Xp`, and `Yp` determines the end points of the intervals (the multi-interval case) ## Examples ```r t<-2 c<-.4 a<-0; b<-10; nx<-10; ny<-4 set.seed(1) Xp<-runif(nx,a,b) Yp<-runif(ny,a,b) IM<-inci.matCS1D(Xp,Yp,t,c) IM dom.num.greedy(IM) dom.num.exact(IM) #might take a long time depending on nx Idom.num.up.bnd(IM,5) Arcs<-arcsCS1D(Xp,Yp,t,c) Arcs summary(Arcs) plot(Arcs) inci.matCS1D(Xp,Yp+10,t,c) t<-2 c<-.4 a<-0; b<-10; #nx is number of X points (target) and ny is number of Y points (nontarget) nx<-20; ny<-4; #try also nx<-40; ny<-10 or nx<-1000; ny<-10; Xp<-runif(nx,a,b) Yp<-runif(ny,a,b) inci.matCS1D(Xp,Yp,t,c) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `inci.matCS1D`, `inci.matPEtri`, and `inci.matPE` ## Author(s) Elvan Ceyhan

inci.matCS1D function