pcds (version 0.1.8)

IarcCSmid.int: The indicator for the presence of an arc from a point to another for Central Similarity Proximity Catch Digraphs (CS-PCDs) - middle 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 \(x\) and is constructed with expansion parameter \(t>0\) and centrality parameter \(c \in (0,1)\) for the interval \((a,b)\).

CS proximity regions are defined with respect to the middle interval int and vertex regions are based on the center associated with the centrality parameter \(c \in (0,1)\). For the interval, int\(=(a,b)\), the parameterized center is \(M_c=a+c(b-a)\). rv is the index of the vertex region \(p_1\) resides, with default=NULL.

If \(p_1\) and \(p_2\) are distinct and either of them are outside interval int, it returns 0, but if they 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

IarcCSmid.int(p1, p2, int, t, c = 0.5, rv = NULL)

Value

\(I(p_2\) 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

Arguments

p1, p2

1D points; \(p_1\) is the point for which the proximity region, \(N_{CS}(p_1,t,c)\) is constructed and \(p_2\) is the point which the function is checking whether its inside \(N_{CS}(p_1,t,c)\) 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 \(M_c=a+c(b-a)\).

rv

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

Author

Elvan Ceyhan

References

See Also

IarcCSend.int, IarcPEmid.int, and IarcPEend.int

Examples

c<-.5
t<-2
a<-0; b<-10; int<-c(a,b)

IarcCSmid.int(7,5,int,t,c)
IarcCSmid.int(7,7,int,t,c)
IarcCSmid.int(7,5,int,t,c=.4)

IarcCSmid.int(1,3,int,t,c)

IarcCSmid.int(9,11,int,t,c)

IarcCSmid.int(19,1,int,t,c)
IarcCSmid.int(19,19,int,t,c)

IarcCSmid.int(3,5,int,t,c)

#or try
Rv<-rel.vert.mid.int(3,int,c)$rv
IarcCSmid.int(3,5,int,t,c,rv=Rv)

IarcCSmid.int(7,5,int,t,c)