pcds (version 0.1.4)

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

Description

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

CS proximity region is constructed with respect to the interval \((a,b)\). This function works whether \(x_1\) and \(x_2\) are inside or outside the interval int.

Vertex regions for middle intervals are based on the center associated with the centrality parameter \(c \in (0,1)\). If \(x_1\) and \(x_2\) are identical, then it returns 1 regardless of their locations (i.e., loops are allowed in the digraph).

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

Usage

IndNCSint(x1, x2, t, c = 0.5, int)

Value

\(I(x_2\) in \(N_{CS}(x_1,t,c))\) for x2, that is, returns 1 if \(x_2\) in \(N_{CS}(x_1,t,c)\), returns 0 otherwise

Arguments

x1

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

x2

A 1D point for which it is checked whether it resides in the proximity region of \(x_1\) or not.

t

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

c

A positive real number in \((0,1)\) parameterizing the center inside int\(=(a,b)\). For the interval, int\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\), and default=0.5.

int

A vector of two real numbers representing an interval.

Author

Elvan Ceyhan

References

See Also

IndNCSmid1D, IndNCSend1D and IndNPEint

Examples

c<-.4
t<-2
a<-0; b<-10; int<-c(a,b)

IndNCSint(7,5,t,c,int)
IndNCSint(17,17,t,c,int)
IndNCSint(15,17,t,c,int)
IndNCSint(1,3,t,c,int)

IndNCSint(-17,17,t,c,int)

IndNCSint(3,5,t,c,int)
IndNCSint(3,3,t,c,int)
IndNCSint(4,5,t,c,int)
IndNCSint(a,5,t,c,int)

c<-.4
r<-2
a<-0; b<-10; int<-c(a,b)

IndNCSint(7,5,t,c,int)