| num.arcsPEstd.tri {pcds} | R Documentation |
Number of arcs of Proportional Edge Proximity Catch Digraphs (PE-PCDs) and quantities related to the triangle - standard equilateral triangle case
Description
An object of class "NumArcs".
Returns the number of arcs of
Proportional Edge Proximity Catch Digraphs (PE-PCDs)
whose vertices are the
given 2D numerical data set, Xp
in the standard equilateral triangle.
It also provides number of vertices
(i.e., number of data points inside the standard equilateral triangle T_e)
and indices of the data points that reside in T_e.
PE proximity region N_{PE}(x,r) 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))
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 T_e;
default is M=(1,1,1), i.e., the center of mass of T_e.
For the number of arcs, loops are not allowed so
arcs are only possible for points inside T_e for this function.
See also (Ceyhan et al. (2006)).
Usage
num.arcsPEstd.tri(Xp, r, M = c(1, 1, 1))
Arguments
Xp |
A set of 2D points which constitute the vertices of the PE-PCD. |
r |
A positive real number
which serves as the expansion parameter for PE proximity region;
must be |
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 |
Value
A list with the elements
desc |
A short description of the output: number of arcs and quantities related to the standard equilateral triangle |
num.arcs |
Number of arcs of the PE-PCD |
tri.num.arcs |
Number of arcs of the induced subdigraph of the PE-PCD
for vertices in the standard equilateral triangle |
num.in.tri |
Number of |
ind.in.tri |
The vector of indices of the |
tess.points |
Tessellation points, i.e., points on which the tessellation of
the study region is performed,
here, tessellation points are the vertices of the support triangle |
vertices |
Vertices of the digraph, |
Author(s)
Elvan Ceyhan
References
Ceyhan E, Priebe CE, Wierman JC (2006).
“Relative density of the random r-factor proximity catch digraphs for testing spatial patterns of segregation and association.”
Computational Statistics & Data Analysis, 50(8), 1925-1964.
See Also
num.arcsPEtri, num.arcsPE,
and num.arcsCSstd.tri
Examples
A<-c(0,0); B<-c(1,0); C<-c(1/2,sqrt(3)/2);
n<-10 #try also n<-20
set.seed(1)
Xp<-runif.std.tri(n)$gen.points
M<-c(.6,.2) #try also M<-c(1,1,1)
Narcs = num.arcsPEstd.tri(Xp,r=1.25,M)
Narcs
summary(Narcs)
oldpar <- par(pty="s")
plot(Narcs,asp=1)
par(oldpar)