# Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case Returns the incidence matrix for the PE-PCD whose vertices are the given 2D numerical data set, `Xp`, in the triangle `tri`$=T(v=1,v=2,v=3)$. PE proximity regions are constructed with respect to triangle `tri` with expansion parameter $r \ge 1$ and vertex regions are based on the center $M=(m_1,m_2)$ in Cartesian coordinates or $M=(\alpha,\beta,\gamma)$ in barycentric coordinates in the interior of the triangle `tri`; default is $M=(1,1,1)$, i.e., the center of mass of `tri`. Loops are allowed, so the diagonal entries are all equal to 1. See also (if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_citeOnly(keys="ceyhan:Phd-thesis,ceyhan:arc-density-PE,ceyhan:dom-num-NPE-Spat2011;textual",package="pcds",cached_env=.Rdpack.currefs) ). ```r inci.matPEtri(Xp, tri, r, M = c(1, 1, 1)) ``` ## Arguments - `Xp`: A set of 2D points which constitute the vertices of PE-PCD. - `tri`: A $3 \times 2$ matrix with each row representing a vertex of the triangle. - `r`: A positive real number which serves as the expansion parameter in PE proximity region; must be $\ge 1$. - `M`: A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates which serves as a center in the interior of the triangle `tri` or the circumcenter of `tri` which may be entered as "CC" as well; default is $M=(1,1,1)$, i.e., the center of mass of `tri`. ## Returns Incidence matrix for the PE-PCD with vertices being 2D data set, `Xp`, in the triangle `tri` with vertex regions based on center `M` ## Examples ```r A<-c(1,1); B<-c(2,0); C<-c(1.5,2); Tr<-rbind(A,B,C); n<-10 set.seed(1) Xp<-runif.tri(n,Tr)$g M<-as.numeric(runif.tri(1,Tr)$g) #try also M<-c(1.6,1.0) IM<-inci.matPEtri(Xp,Tr,r=1.25,M) IM dom.num.greedy(IM) #try also dom.num.exact(IM) Idom.num.up.bnd(IM,3) ``` ## References if(!exists(".Rdpack.currefs")) .Rdpack.currefs \<-new.env();Rdpack::insert_all_ref(.Rdpack.currefs) ## See Also `inci.matPE`, `inci.matCStri`, and `inci.matAStri` ## Author(s) Elvan Ceyhan

inci.matPEtri function