pcds (version 0.1.8)

IarcPEend.int: 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 \(I(p_2 \in N_{PE}(p_1,r))\) for points \(p_1\) and \(p_2\), that is, returns 1 if \(p_2\) is in \(N_{PE}(p_1,r)\), 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 \(p_1\) resides, with default=NULL, and rv=1 for left end-interval and rv=2 for the right end-interval. If \(p_1\) and \(p_2\) 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

IarcPEend.int(p1, p2, int, r, rv = NULL)

Value

\(I(p_2 \in N_{PE}(p_1,r))\) for points \(p_1\) and \(p_2\), that is, returns 1 if \(p_2\) is in \(N_{PE}(p_1,r)\)

(i.e., if there is an arc from \(p_1\) to \(p_2\)), returns 0 otherwise

Arguments

p1

A 1D point whose PE proximity region is constructed.

p2

A 1D point. The function determines whether \(p_2\) is inside the PE proximity region of \(p_1\) or not.

int

A vector of two real numbers representing an interval.

r

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

rv

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

Author

Elvan Ceyhan

References

See Also

IarcPEmid.int, IarcCSmid.int, and IarcCSend.int

Examples

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

IarcPEend.int(15,17,int,r)
IarcPEend.int(1.5,17,int,r)
IarcPEend.int(-15,17,int,r)