pcds (version 0.1.2)

IndNCSend1D: The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - end interval case

Description

Returns \(I(x_2\) in \(N_{CS}(x_1,t))\) for points \(x_1\) and \(x_2\), that is, returns 1 if \(x_2\) is in \(N_{CS}(x_1,t)\), returns 0 otherwise, where \(N_{CS}(x,t)\) is the CS proximity region for point \(x\) with expansion parameter \(t>0\) for the region outside the interval \((a,b)\).

rv is the index of the end vertex region \(x_1\) resides, with default=NULL, and rv=1 for left end interval and rv=2 for the right end interval. If \(x_1\) and \(x_2\) are distinct and either of them are inside interval int, it returns 0, but if they are identical, then it returns 1 regardless of their locations (i.e., it allows loops).

See also (ceyhan:revstat-2016;textualpcds).

Usage

IndNCSend1D(x1, x2, t, int, rv = NULL)

Arguments

x1

A 1D point for which the CS proximity region is constructed.

x2

A 1D point to check whether it is inside the proximity region or not.

t

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

int

A vector of two real numbers representing an interval.

rv

Index of the end interval containing the point, either 1,2 or NULL (default=NULL).

Value

\(I(x_2\) in \(N_{CS}(x_1,t))\) for points \(x_1\) and \(x_2\), that is, returns 1 if \(x_2\) is in \(N_{CS}(x_1,t)\) (i.e., if there is an arc from \(x_1\) to \(x_2\)), returns 0 otherwise

References

See Also

IndNCSmid1D, IndNPEmid1D, and IndNPEend1D

Examples

# NOT RUN {
a<-0; b<-10; int<-c(a,b)
t<-2

IndNCSend1D(15,17,t,int)
IndNCSend1D(15,15,t,int)

IndNCSend1D(1.5,17,t,int)
IndNCSend1D(1.5,1.5,t,int)

IndNCSend1D(-15,17,t,int)

IndNCSend1D(-15,-17,t,int)

a<-0; b<-10; int<-c(a,b)
t<-.5

IndNCSend1D(15,17,t,int)

# }