pcds (version 0.1.4)

IncMatCSTe: Incidence matrix for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

Description

Returns the incidence matrix for the CS-PCD whose vertices are the given 2D numerical data set, dat, in the standard equilateral triangle \(T_e=T(v=1,v=2,v=3)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\).

CS proximity region is defined with respect to the standard equilateral triangle \(T_e=T(v=1,v=2,v=3)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\) and edge 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 \(T_e\); default is \(M=(1,1,1)\) i.e., the center of mass of \(T_e\). Loops are allowed, so the diagonal entries are all equal to 1.

See also (ceyhan:Phd-thesis,ceyhan:arc-density-CS,ceyhan:test2014;textualpcds).

Usage

IncMatCSTe(dat, t, M = c(1, 1, 1))

Value

Incidence matrix for the CS-PCD with vertices being 2D data set, dat and CS proximity regions are defined in the standard equilateral triangle \(T_e\) with M-edge regions.

Arguments

dat

A set of 2D points which constitute the vertices of the CS-PCD.

t

A positive real number which serves as the expansion parameter in CS proximity region.

M

A 2D point in Cartesian coordinates or a 3D point in barycentric coordinates. which serves as a center in the interior of the standard equilateral triangle \(T_e\); default is \(M=(1,1,1)\) i.e. the center of mass of \(T_e\).

Author

Elvan Ceyhan

References

See Also

IncMatCStri, IncMatCSMT and IncMatPETe

Examples

A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
Te<-rbind(A,B,C);
n<-10

set.seed(1)
dat<-runifTe(n)$gen.points

M<-as.numeric(runifTe(1)$g)  #try also M<-c(.6,.2)

NumArcsCSTe(dat,t=1.25)

inc.mat<-IncMatCSTe(dat,t=1.25,M)
inc.mat
sum(inc.mat)-n

dom.greedy(inc.mat)
# \donttest{
dom.exact(inc.mat)  #might take a long time for large n
# }
IndUBdom(inc.mat,1)

inc.mat<-IncMatCSTe(rbind(dat,c(0,1)),t=1.25,M)
inc.mat
sum(inc.mat)-(n+1)

IncMatCSTe(dat,t=1.5,M);

IncMatCSTe(rbind(dat,dat),t=1.5,M)

dat.fr<-data.frame(a=dat)
IncMatCSTe(dat.fr,t=1.5,M);