Idom.num2PEbasic.tri: The indicator for two points being a dominating set for...
| Idom.num2PEbasic.tri | R Documentation |
The indicator for two points being a dominating set for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - standard basic triangle case
Description
Returns I({p1,p2} is
a dominating set of the PE-PCD)
where the vertices of the PE-PCD are the 2D data set Xp
in the standard basic triangle
T_b=T((0,0),(1,0),(c_1,c_2)),
that is, returns 1 if {p1,p2} is a dominating set of PE-PCD,
and returns 0 otherwise.
PE proximity regions are defined with respect to T_b.
In the standard basic triangle, T_b,
c_1 is in [0,1/2], c_2>0
and (1-c_1)^2+c_2^2 \le 1.
Any given triangle can be mapped to the standard basic triangle by a combination of rigid body motions (i.e., translation, rotation and reflection) and scaling, preserving uniformity of the points in the original triangle. Hence, standard basic triangle is useful for simulation studies under the uniformity hypothesis.
Vertex regions are based on center M=(m_1,m_2) in Cartesian
coordinates or M=(\alpha,\beta,\gamma) in barycentric coordinates
in the interior of a standard basic triangle T_b;
default is M=(1,1,1), i.e., the center of mass of T_b.
Point, p1,
is in the vertex region of vertex rv1
(default is NULL);
and point, p2,
is in the vertex region of vertex rv2
(default is NULL);
vertices are labeled as 1,2,3
in the order they are stacked row-wise.
ch.data.pnts is for checking
whether points p1 and p2 are both data points
in Xp or not (default is FALSE),
so by default this function checks
whether the points p1 and p2 would constitute
a dominating set
if they both were actually in the data set.
See also (\insertCiteceyhan:Phd-thesis,ceyhan:dom-num-NPE-Spat2011;textualpcds).
Usage
Idom.num2PEbasic.tri(
p1,
p2,
Xp,
r,
c1,
c2,
M = c(1, 1, 1),
rv1 = NULL,
rv2 = NULL,
ch.data.pnts = FALSE
)
Arguments
p1, p2 |
Two 2D points to be tested for constituting a dominating set of the PE-PCD. |
Xp |
A set of 2D points which constitutes the vertices of the PE-PCD. |
r |
A positive real number
which serves as the expansion parameter in PE proximity region;
must be |
c1, c2 |
Positive real numbers
which constitute the vertex of the standard basic triangle.
adjacent to the shorter edges; |
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 basic triangle |
rv1, rv2 |
The indices of the vertices
whose regions contains |
ch.data.pnts |
A logical argument for
checking whether points |
Value
I({p1,p2} is a dominating set of the PE-PCD)
where the vertices of the PE-PCD are the 2D data set Xp,
that is, returns 1 if {p1,p2} is a dominating set of PE-PCD,
and returns 0 otherwise.
Author(s)
Elvan Ceyhan
References
\insertAllCitedSee Also
Idom.num2PEtri, Idom.num2ASbasic.tri,
and Idom.num2AStri
Examples
c1<-.4; c2<-.6;
A<-c(0,0); B<-c(1,0); C<-c(c1,c2);
Tb<-rbind(A,B,C)
n<-10 #try also n<-20
set.seed(1)
Xp<-runif.basic.tri(n,c1,c2)$g
M<-as.numeric(runif.basic.tri(1,c1,c2)$g) #try also M<-c(.6,.3)
r<-2
Idom.num2PEbasic.tri(Xp[1,],Xp[2,],Xp,r,c1,c2,M)
Idom.num2PEbasic.tri(c(1,2),c(1,3),rbind(c(1,2),c(1,3)),r,c1,c2,M)
Idom.num2PEbasic.tri(c(1,2),c(1,3),rbind(c(1,2),c(1,3)),r,c1,c2,M,
ch.data.pnts = TRUE)
ind.gam2<-vector()
for (i in 1:(n-1))
for (j in (i+1):n)
{if (Idom.num2PEbasic.tri(Xp[i,],Xp[j,],Xp,r,c1,c2,M)==1)
ind.gam2<-rbind(ind.gam2,c(i,j))}
ind.gam2
#or try
rv1<-rel.vert.basic.tri(Xp[1,],c1,c2,M)$rv;
rv2<-rel.vert.basic.tri(Xp[2,],c1,c2,M)$rv;
Idom.num2PEbasic.tri(Xp[1,],Xp[2,],Xp,r,c1,c2,M,rv1,rv2)
#or try
rv1<-rel.vert.basic.tri(Xp[1,],c1,c2,M)$rv;
Idom.num2PEbasic.tri(Xp[1,],Xp[2,],Xp,r,c1,c2,M,rv1)
#or try
rv2<-rel.vert.basic.tri(Xp[2,],c1,c2,M)$rv;
Idom.num2PEbasic.tri(Xp[1,],Xp[2,],Xp,r,c1,c2,M,rv2=rv2)
Idom.num2PEbasic.tri(c(1,2),Xp[2,],Xp,r,c1,c2,M,ch.data.pnts = FALSE)
#gives an error message if ch.data.pnts = TRUE since not both points are data points in Xp
