pcds (version 0.1.4)

IndNPEend1D: The indicator for the presence of an arc from a point to another for Proportional Edge Proximity Catch Digraphs (PE-PCDs) - end interval case

Description

Returns \(I(x_2 \in N_{PE}(x_1,r))\) for points \(x_1\) and \(x_2\), that is, returns 1 if \(x_2\) is in \(N_{PE}(x_1,r)\), returns 0 otherwise, where \(N_{PE}(x,r)\) is the PE proximity region for point \(x\) with expansion parameter \(r \ge 1\) 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:metrika-2012;textualpcds).

Usage

IndNPEend1D(x1, x2, r, int, rv = NULL)

Value

\(I(x_2 \in N_{PE}(x_1,r))\) for points \(x_1\) and \(x_2\), that is, returns 1 if \(x_2\) is in \(N_{PE}(x_1,r)\)

(i.e., if there is an arc from \(x_1\) to \(x_2\)), returns 0 otherwise

Arguments

x1

A 1D point whose PE proximity region is constructed.

x2

A 1D point. The function determines whether \(x_2\) is inside the PE proximity region of \(x_1\) or not.

r

A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).

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 is NULL).

Author

Elvan Ceyhan

References

See Also

IndNPEmid1D, IndNCSmid1D, and IndNCSend1D

Examples

a<-0; b<-10; int<-c(a,b)
r<-2

IndNPEend1D(15,17,r,int)
IndNPEend1D(15,15,r,int)

IndNPEend1D(1.5,17,r,int)

IndNPEend1D(-15,17,r,int)

IndNPEend1D(a,17,r,int)
IndNPEend1D(15,17,r=1.1,int)

a<-0; b<-10; int<-c(a,b)
r<-2
IndNPEend1D(15,17,r,int)