Returns \(I(p_2 \in N_{PE}(p_1,r,c))\) for points \(p_1\) and \(p_2\), that is, returns 1 if \(p_2\) is in \(N_{PE}(p_1,r,c)\), returns 0 otherwise, where \(N_{PE}(x,r,c)\) is the PE proximity region for point \(x\) and is constructed with expansion parameter \(r \ge 1\) and centrality parameter \(c \in (0,1)\) for the interval \((a,b)\).
PE 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:metrika-2012,ceyhan:revstat-2016;textualpcds).
IarcPEmid.int(p1, x2, int, r, c = 0.5, rv = NULL)\(I(p_2 \in N_{PE}(p_1,r,c))\) for points \(p_1\) and \(p_2\) that is, returns 1 if \(p_2\) is in \(N_{PE}(p_1,r,c)\), returns 0 otherwise
1D points; \(p_1\) is the point for which the proximity region, \(N_{PE}(p_1,r,c)\) is constructed and \(p_2\) is the point which the function is checking whether its inside \(N_{PE}(p_1,r,c)\) or not.
A vector of two real numbers representing an interval.
A positive real number which serves as the expansion parameter in PE proximity region; must be \(\ge 1\).
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 \(M_c=a+c(b-a)\).
The index of the vertex region \(p_1\) resides, with default=NULL.
Elvan Ceyhan
IarcPEend.int, IarcCSmid.int, and IarcCSend.int
c<-.4
r<-2
a<-0; b<-10; int<-c(a,b)
IarcPEmid.int(7,5,int,r,c)
IarcPEmid.int(1,3,int,r,c)
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