# The closest points to center in each vertex region in an interval An object of class `"Extrema"`. Returns the closest data points among the data set, `Xp`, in each $M_c$-vertex region i.e., finds the closest points from right and left to $M_c$ among points of the 1D data set `Xp` which reside in in the interval `int`$=(a,b)$. $M_c$ is based on the centrality parameter $c \in (0,1)$, so that $100c$ % of the length of interval is to the left of $M_c$ and $100(1-c)$ % of the length of the interval is to the right of $M_c$. That is, for the interval $(a,b)$, $M_c=a+c(b-a)$. If there are no points from `Xp` to the left of $M_c$ in the interval, then it yields `NA`, and likewise for the right of $M_c$ in the interval. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:metrika-2012;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r cl2Mc.int(Xp, int, c) ``` ## Arguments - `Xp`: A set or `vector` of 1D points from which closest points to $M_c$ are found in the interval `int`. - `int`: A `vector` of two real numbers representing an interval. - `c`: A positive real number in $(0,1)$ parameterizing the center inside `int`$=(a,b)$. For the interval, `int`$=(a,b)$, the parameterized center is $M_c=a+c(b-a)$. ## Returns A `list` with the elements - **txt1**: Vertex Labels are $a=1$ and $b=2$ for the interval $(a,b)$. - **txt2**: A short description of the distances as `"Distances from ..."` - **type**: Type of the extrema points - **desc**: A short description of the extrema points - **mtitle**: The `"main"` title for the plot of the extrema - **ext**: The extrema points, here, closest points to $M_c$ in each vertex region - **ind.ext**: The data indices of extrema points, `ext`. - **X**: The input data vector, `Xp`. - **num.points**: The number of data points, i.e., size of `Xp` - **supp**: Support of the data points, here, it is `int`. - **cent**: The (parameterized) center point used for construction of vertex regions. - **ncent**: Name of the (parameterized) center, `cent`, it is `"Mc"` for this function. - **regions**: Vertex regions inside the interval, `int`, provided as a list. - **region.names**: Names of the vertex regions as `"vr=1"`, `"vr=2"` - **region.centers**: Centers of mass of the vertex regions inside `int`. - **dist2ref**: Distances from closest points in each vertex region to $M_c$. ## Examples ```r c<-.4 a<-0; b<-10; int<-c(a,b) Mc<-centerMc(int,c) nx<-10 xr<-range(a,b,Mc) xf<-(xr[2]-xr[1])*.5 Xp<-runif(nx,a,b) Ext<-cl2Mc.int(Xp,int,c) Ext summary(Ext) plot(Ext) cMc<-Ext Xlim<-range(a,b,Xp) xd<-Xlim[2]-Xlim[1] plot(cbind(a,0),xlab="",pch=".", main=paste("Closest Points in Mc-Vertex Regions \n to the Center Mc = ",Mc,sep=""), 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(c(cMc$ext),0),pch=4,col=2) text(cbind(c(a,b,Mc)-.02*xd,-0.05),c("a","b",expression(M[c]))) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `cl2CCvert.reg.basic.tri` and `cl2CCvert.reg` ## Author(s) Elvan Ceyhan

cl2Mc.int function