pcds (version 0.1.6)

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

Description

Returns the incidence matrix for the PE-PCD whose vertices are the given 3D numerical data set, Xp, in the tetrahedron \(th=T(v=1,v=2,v=3,v=4)\).

PE proximity regions are constructed with respect to tetrahedron th with expansion parameter \(r \ge 1\) and vertex regions are based on the center M which is circumcenter ("CC") or center of mass ("CM") of th with default="CM". Loops are allowed, so the diagonal entries are all equal to 1.

See also (ceyhan:Phd-thesis,ceyhan:comp-geo-2010;textualpcds).

Usage

IncMatPEtetra(Xp, th, r, M = "CM")

Value

Incidence matrix for the PE-PCD with vertices being 3D data set, Xp, in the tetrahedron th with vertex regions based on circumcenter or center of mass

Arguments

Xp

A set of 3D points which constitute the vertices of PE-PCD.

th

A \(4 \times 3\) matrix with each row representing a vertex of the tetrahedron.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

M

The center to be used in the construction of the vertex regions in the tetrahedron, th. Currently it only takes "CC" for circumcenter and "CM" for center of mass; default="CM".

Author

Elvan Ceyhan

References

See Also

IncMatPEtri, IncMatPE1D, and IncMatPE

Examples

if (FALSE) {
A<-c(0,0,0); B<-c(1,0,0); C<-c(1/2,sqrt(3)/2,0); D<-c(1/2,sqrt(3)/6,sqrt(6)/3)
tetra<-rbind(A,B,C,D)
n<-5

Xp<-runif.tetra(n,tetra)$g  #try also Xp<-c(.5,.5,.5)

M<-"CM"  #try also M<-"CC"
r<-1.5

IM<-IncMatPEtetra(Xp,tetra,r=1.25)  #uses the default M="CM"
IM<-IncMatPEtetra(Xp,tetra,r=1.25,M)
IM
dom.greedy(IM)
IndUBdom(IM,3) #try also dom.exact(IM)  #this might take a long time for large n
}