pcds (version 0.1.8)

IarcCSint: 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 \(I(p_2\) in \(N_{CS}(p_1,t,c))\) for points \(p_1\) and \(p_2\), that is, returns 1 if \(p_2\) is in \(N_{CS}(p_1,t,c)\), 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 \(p_1\) and \(p_2\) 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 \(p_1\) and \(p_2\) 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

IarcCSint(p1, p2, int, t, c = 0.5)

Value

\(I(p_2\) in \(N_{CS}(p_1,t,c))\) for p2, that is, returns 1 if \(p_2\) in \(N_{CS}(p_1,t,c)\), returns 0 otherwise

Arguments

p1

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

p2

A 1D point for which it is checked whether it resides in the proximity region of \(p_1\) or not.

int

A vector of two real numbers representing an interval.

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\(=(a,b)\) with the default c=.5. For the interval, int\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\).

Author

Elvan Ceyhan

References

See Also

IarcCSmid.int, IarcCSend.int and IarcPEint

Examples

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

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

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

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

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

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