pcds (version 0.1.2)

funsCSGamTe: The function GamkCSTe is for \(k\) (\(k=2,3,4,5\)) points constituting a dominating set for Central Similarity Proximity Catch Digraphs (CS-PCDs) - standard equilateral triangle case

Description

Four indicator functions: Gam2CSTe, Gam3CSTe, Gam4CSTe, Gam5CSTe and Gam6CSTe.

The function GamkCSTe returns I({pt1,...,ptk} is a dominating set of the CS-PCD) where vertices of CS-PCD are the 2D data set Dt, that is, returns 1 if {pt1,...,ptk} is a dominating set of CS-PCD, returns 0 otherwise for \(k=2,3,4,5,6\).

CS proximity region is constructed with respect to \(T_e=T(A,B,C)=T((0,0),(1,0),(1/2,\sqrt{3}/2))\) with expansion parameter \(t>0\) and edge regions are based on center of mass \(CM=(1/2,\sqrt{3}/6)\).

ch.data.pnts is for checking whether points pt1,...,ptk are data points in Dt or not (default is FALSE), so by default this function checks whether the points pt1,...,ptk would be a dominating set if they actually were in the data set.

See also (ceyhan:Phd-thesis,ceyhan:comp-geo-2010,ceyhan:mcap2012;textualpcds).

Usage

Gam2CSTe(pt1, pt2, Dt, t, ch.data.pnts = FALSE)
Gam3CSTe(pt1, pt2, pt3, Dt, t, ch.data.pnts = FALSE)
Gam4CSTe(pt1, pt2, pt3, pt4, Dt, t, ch.data.pnts = FALSE)
Gam5CSTe(pt1, pt2, pt3, pt4, pt5, Dt, t, ch.data.pnts = FALSE)
Gam6CSTe(pt1, pt2, pt3, pt4, pt5, pt6, Dt, t, ch.data.pnts = FALSE)

Arguments

pt1, pt2, pt3, pt4, pt5, pt6

The points {\(pt1,\ldots,ptk\)} are \(k\) 2D points (for \(k=2,3,4,5,6\)) to be tested for constituting a dominating set of the CS-PCD.

Dt

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

t

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

ch.data.pnts

A logical argument for checking whether points {\(pt1,\ldots,ptk\)} are data points in Dt or not (default is FALSE).

Value

The function GamkCSTe returns {pt1,...,ptk} is a dominating set of the CS-PCD) where vertices of the CS-PCD are the 2D data set Dt), that is, returns 1 if {pt1,...,ptk} is a dominating set of CS-PCD, returns 0 otherwise.

See Also

Gam1CSTe, Gam2PEtri and Gam2PEtetra

Examples

# NOT RUN {
set.seed(123)
#Examples for Gam2CSTe
t<-1.5
n<-9 #try also 10, 20 (it may take longer for larger n)

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

Gam2CSTe(dat[1,],dat[2,],dat,t)
Gam2CSTe(dat[1,],dat[1,],dat,t)

Gam2CSTe(dat[1,],dat[3,],dat,t)

Gam2CSTe(c(.2,.2),dat[2,],dat,t)

Gam2CSTe(c(.2,.2),c(.2,.3),dat,t)

Gam2CSTe(c(.2,.2),c(.2,.3),rbind(c(.2,.2),c(.2,.3)),t)
Gam2CSTe(c(1.2,1.2),c(1.2,1.3),rbind(c(1.2,1.2),c(1.2,1.3)),t)

ind.gam2<-vector()
for (i in 1:(n-1))
 for (j in (i+1):n)
 {if (Gam2CSTe(dat[i,],dat[j,],dat,t)==1)
  ind.gam2<-rbind(ind.gam2,c(i,j))}

ind.gam2

P1<-c(.4,.2); P2<-c(.6,.4)
Gam2CSTe(P1,P2,dat,t)

dat.fr<-data.frame(a=dat)
Gam2CSTe(P1,P2,dat.fr,t)

Gam2CSTe(c(.2,.2),dat[2,],dat,t,ch.data.pnts = FALSE)
#will give an error message if ch.data.pnts = TRUE
#since not both points are data points in Dt

Gam2CSTe(c(.2,.2),c(.2,.3),dat,t,ch.data.pnts = FALSE)
#will give an error message if ch.data.pnts = TRUE
#since not both points are data points in Dt

#Examples for Gam3CSTe
t<-1.5
n<-9 #try also 10, 20 (it may take longer for larger n)

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

Gam3CSTe(dat[1,],dat[2,],dat[3,],dat,t)

Gam3CSTe(dat[1,],dat[3,],dat[4,],dat,t)

Gam3CSTe(c(.2,.2),dat[2,],dat[3,],dat,t)

Gam3CSTe(c(.2,.2),c(.2,.3),c(.2,.4),rbind(c(.2,.2),c(.2,.3),c(.2,.4)),t)
Gam3CSTe(c(1.2,1.2),c(1.2,1.3),c(1.2,1.4),rbind(c(1.2,1.2),c(1.2,1.3),c(1.2,1.4)),t)

ind.gam3<-vector()
for (i in 1:(n-2))
 for (j in (i+1):(n-1))
   for (k in (j+1):n)
   {if (Gam3CSTe(dat[i,],dat[j,],dat[k,],dat,t)==1)
    ind.gam3<-rbind(ind.gam3,c(i,j,k))}

ind.gam3

P1<-c(.4,.2); P2<-c(.6,.4); P3<-c(.5,.1)
Gam3CSTe(P1,P2,P3,dat,t)

dat.fr<-data.frame(a=dat)
Gam3CSTe(P1,P2,P3,dat.fr,t)

Gam3CSTe(c(.2,.2),dat[2,],dat[3,],dat,t,ch.data.pnts = FALSE)
#gives an error message if ch.data.pnts = TRUE
#since not all points, pt1, pt2, and pt3, are data points in Dt

#Examples for Gam4CSTe
t<-1.5
n<-9 #try also 10, 20 (it may take longer for larger n)

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

Gam4CSTe(dat[1,],dat[2,],dat[3,],dat[4,],dat,t)

Gam4CSTe(dat[1,],dat[3,],dat[4,],dat[5,],dat,t)

Gam4CSTe(c(.2,.2),dat[2,],dat[3,],dat[4,],dat,t)

Gam4CSTe(c(.2,.2),c(.2,.3),c(.2,.4),c(.2,.5),rbind(c(.2,.2),c(.2,.3),c(.2,.4),c(.2,.5)) ,t)
Gam4CSTe(c(1.2,1.2),c(1.2,1.3),c(1.2,1.4),c(1.2,1.5),
rbind(c(1.2,1.2),c(1.2,1.3),c(1.2,1.4),c(1.2,1.5)),t)

ind.gam4<-vector()
for (i in 1:(n-3))
 for (j in (i+1):(n-2))
   for (k in (j+1):(n-1))
     for (l in (k+1):n)
     {if (Gam4CSTe(dat[i,],dat[j,],dat[k,],dat[l,],dat,t)==1)
      ind.gam4<-rbind(ind.gam4,c(i,j,k,l))}

ind.gam4

P1<-c(.4,.2); P2<-c(.6,.4); P3<-c(.5,.1); P4<-c(.5,.29)
Gam4CSTe(P1,P2,P3,P4,dat,t)

dat.fr<-data.frame(a=dat)
Gam4CSTe(P1,P2,P3,P4,dat.fr,t)

Gam4CSTe(c(.2,.2),dat[2,],dat[3,],dat[4,],dat,t,ch.data.pnts = FALSE)
#gives an error message if ch.data.pnts = TRUE since not all points are data points in Dt

#Examples for Gam5CSTe
t<-1.5
n<-9 #try also 10, 20 (it may take longer for larger n)

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

Gam5CSTe(dat[1,],dat[2,],dat[3,],dat[4,],dat[5,],dat,t)

Gam5CSTe(dat[1,],dat[3,],dat[4,],dat[5,],dat[6,],dat,t)

Gam5CSTe(c(.2,.2),dat[2,],dat[3,],dat[4,],dat[5,],dat,t)

ind.gam5<-vector()
for (i1 in 1:(n-4))
 for (i2 in (i1+1):(n-3))
   for (i3 in (i2+1):(n-2))
     for (i4 in (i3+1):(n-1))
       for (i5 in (i4+1):n)
       {if (Gam5CSTe(dat[i1,],dat[i2,],dat[i3,],dat[i4,],dat[i5,],dat,t)==1)
        ind.gam5<-rbind(ind.gam5,c(i1,i2,i3,i4,i5))}

ind.gam5

P1<-c(.4,.2); P2<-c(.6,.4); P3<-c(.5,.1); P4<-c(.5,.29); P5<-c(.3,.3)
Gam5CSTe(P1,P2,P3,P4,P5,dat,t)

dat.fr<-data.frame(a=dat)
Gam5CSTe(P1,P2,P3,P4,P5,dat.fr,t)

Gam5CSTe(c(.2,.2),dat[2,],dat[3,],dat[4,],dat[5,],dat,t,ch.data.pnts = FALSE)
#gives an error message if ch.data.pnts = TRUE since not all points are data points in Dt

#Examples for Gam6CSTe
t<-1.5
n<-9 #try also 10, 20 (it may take longer for larger n)

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

Gam6CSTe(dat[1,],dat[2,],dat[3,],dat[4,],dat[5,],dat[6,],dat,t)

Gam6CSTe(dat[1,],dat[3,],dat[4,],dat[5,],dat[6,],dat[7,],dat,t)

Gam6CSTe(c(.2,.2),dat[2,],dat[3,],dat[4,],dat[5,],dat[6,],dat,t)

ind.gam6<-vector()
for (i1 in 1:(n-5))
 for (i2 in (i1+1):(n-4))
   for (i3 in (i2+1):(n-3))
     for (i4 in (i3+1):(n-2))
       for (i5 in (i4+1):(n-1))
         for (i6 in (i5+1):n)
         {if (Gam6CSTe(dat[i1,],dat[i2,],dat[i3,],dat[i4,],dat[i5,],dat[i6,],dat,t)==1)
          ind.gam6<-rbind(ind.gam6,c(i1,i2,i3,i4,i5,i6))}

ind.gam6

P1<-c(.4,.2); P2<-c(.6,.4); P3<-c(.5,.1); P4<-c(.5,.29); P5<-c(.3,.3); P6<-c(.4,.4)
Gam6CSTe(P1,P2,P3,P4,P5,P6,dat,t)

dat.fr<-data.frame(a=dat)
Gam6CSTe(P1,P2,P3,P4,P5,P6,dat.fr,t)

Gam6CSTe(c(.2,.2),dat[2,],dat[3,],dat[4,],dat[5,],dat[6,],dat,t,ch.data.pnts = FALSE)
#gives an error message if ch.data.pnts = TRUE since not all points are data points in Dt

# }