# The arcs of Central Similarity Proximity Catch Digraph (CS-PCD) for 1D data - middle intervals case An object of class `"PCDs"`. Returns arcs of CS-PCD as tails (or sources) and heads (or arrow ends) and related parameters and the quantities of the digraph. The vertices of the CS-PCD are the 1D data points in `Xp` in the middle interval case. For this function, CS proximity regions are constructed with respect to the intervals based on `Yp` points with expansion parameter $t>0$ and centrality parameter $c \in (0,1)$. That is, for this function, arcs may exist for points only inside the intervals. It also provides various descriptions and quantities about the arcs of the CS-PCD such as number of arcs, arc density, etc. Vertex regions are based on center $M_c$ of each middle interval. 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 arcsCSmid.int(Xp, Yp, t, c = 0.5) ``` ## Arguments - `Xp`: A set or `vector` of 1D points which constitute the vertices of the CS-PCD. - `Yp`: A set or `vector` of 1D points which constitute the end points of the intervals. - `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 A `list` with the elements - **type**: A description of the type of the digraph - **parameters**: Parameters of the digraph, here, they are expansion and centrality parameters. - **tess.points**: Points on which the tessellation of the study region is performed, here, tessellation is the intervalization based on `Yp` points. - **tess.name**: Name of the tessellation points `tess.points` - **vertices**: Vertices of the digraph, i.e., `Xp` points - **vert.name**: Name of the data set which constitute the vertices of the digraph - **S**: Tails (or sources) of the arcs of CS-PCD for 1D data in the middle intervals - **E**: Heads (or arrow ends) of the arcs of CS-PCD for 1D data in the middle intervals - **mtitle**: Text for `"main"` title in the plot of the digraph - **quant**: Various quantities for the digraph: number of vertices, number of partition points, number of intervals, number of arcs, and arc density. ## Examples ```r t<-1.5 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; set.seed(1) Xp<-runif(nx,a,b) Yp<-runif(ny,a,b) arcsCSmid.int(Xp,Yp,t,c) arcsCSmid.int(Xp,Yp+10,t,c) Arcs<-arcsCSmid.int(Xp,Yp,t,c) Arcs summary(Arcs) plot(Arcs) S<-Arcs$S E<-Arcs$E jit<-.1 yjit<-runif(nx,-jit,jit) Xlim<-range(Xp,Yp) xd<-Xlim[2]-Xlim[1] plot(cbind(a,0), main="arcs of CS-PCD whose vertices (jittered along y-axis)\n in middle intervals ", xlab=" ", ylab=" ", xlim=Xlim+xd*c(-.05,.05),ylim=3*c(-jit,jit),pch=".") abline(h=0,lty=1) points(Xp, yjit,pch=".",cex=3) abline(v=Yp,lty=2) arrows(S, yjit, E, yjit, length = .05, col= 4) t<-.5 c<-.4 a<-0; b<-10; 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) arcsCSmid.int(Xp,Yp,t,c) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `arcsPEend.int`, `arcsPE1D`, `arcsCSmid.int`, `arcsCSend.int` and `arcsCS1D` ## Author(s) Elvan Ceyhan

arcsCSmid.int function