pcds (version 0.1.6)

IncMatPEtri: Incidence matrix for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - one triangle case

Description

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 (ceyhan:Phd-thesis,ceyhan:arc-density-PE,ceyhan:dom-num-NPE-Spat2011;textualpcds).

Usage

IncMatPEtri(Xp, tri, r, M = c(1, 1, 1))

Value

Incidence matrix for the PE-PCD with vertices being 2D data set, Xp, in the triangle tri with vertex regions based on center M

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.

Author

Elvan Ceyhan

References

See Also

IncMatPE, IncMatCStri, and IncMatAStri

Examples

if (FALSE) {
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<-IncMatPEtri(Xp,Tr,r=1.25,M)

IM
dom.greedy(IM) #try also dom.exact(IM)
IndUBdom(IM,3)
}