inci.mat.undCStri {pcds.ugraph} | R Documentation |
Incidence matrix for the underlying or reflexivity graphs of Central Similarity Proximity Catch Digraphs (CS-PCDs) - one triangle case
Description
Returns the incidence matrix
for the underlying or reflexivity graphs of the CS-PCD
whose vertices are the given 2D numerical data set, Xp
,
in the triangle tri
.
CS proximity regions are constructed with respect to triangle tri
with expansion parameter
and edge regions are based on the center
in Cartesian coordinates
or
in barycentric coordinates
in the interior of the triangle
tri
;
default is , i.e., the center of mass of
tri
.
Loops are allowed, so the diagonal entries are all equal to 1.
See also (Ceyhan (2005, 2016)).
Usage
inci.mat.undCStri(
Xp,
tri,
t,
M = c(1, 1, 1),
ugraph = c("underlying", "reflexivity")
)
Arguments
Xp |
A set of 2D points which constitute the vertices of the underlying or reflexivity graph of the CS-PCD. |
tri |
A |
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 triangle |
ugraph |
The type of the graph based on CS-PCDs,
|
Value
Incidence matrix for the underlying or reflexivity graphs
of the CS-PCD with vertices
being 2D data set, Xp
in the triangle tri
with edge regions based on center M
Author(s)
Elvan Ceyhan
References
Ceyhan E (2005).
An Investigation of Proximity Catch Digraphs in Delaunay Tessellations, also available as technical monograph titled Proximity Catch Digraphs: Auxiliary Tools, Properties, and Applications.
Ph.D. thesis, The Johns Hopkins University, Baltimore, MD, 21218.
Ceyhan E (2016).
“Edge Density of New Graph Types Based on a Random Digraph Family.”
Statistical Methodology, 33, 31-54.
See Also
inci.mat.undCS
, inci.mat.undAStri
,
inci.mat.undPEtri
, and inci.matCStri
Examples
#\donttest{
A<-c(1,1); B<-c(2,0); C<-c(1.5,2);
Tr<-rbind(A,B,C);
n<-10
set.seed(1)
Xp<-pcds::runif.tri(n,Tr)$g
M<-as.numeric(pcds::runif.tri(1,Tr)$g)
(IM<-inci.mat.undCStri(Xp,Tr,t=1.5,M))
pcds::dom.num.greedy(IM)
pcds::Idom.num.up.bnd(IM,3)
(IM<-inci.mat.undCStri(Xp,Tr,t=1.5,M,ugraph="r"))
pcds::dom.num.greedy(IM)
pcds::Idom.num.up.bnd(IM,3)
#}