IsoCheck (version 0.1.0)

checkStarEquivalence: Checking the Equivalence of Two Stars

Description

This function checks the equivalence of two balanced covering stars of PG(n-1,2) by comparing sorted bitstring representations.

Usage

checkStarEquivalence(star1, star2)

Arguments

star1

A star of PG(n-1,2) stored as a three dimensional binary array (see Details and Examples of checkSpreadEquivalence).

star2

A star of PG(n-1,2) stored as a three dimensional binary array (see Details and Examples of checkSpreadEquivalence).

Value

A Boolean indicating whether or not the two stars are equivalent.

Details

This code checks if two stars of PG(n-1,2) are equivalent using the bitstring representation of Spencer et al. (2019). Both input stars should be formatted as 3-dimensional arrays with spread1[i,j,k] indicating whether or not the ith basic factor is present in the jth effect of the kth flat of spread1.

References

Spencer, N.A., Ranjan, P., and Mendivil, F., (2019), "Isomorphism Check for \(2^n\) Factorial Designs with Randomization Restrictions", Journal of Statistical Theory and Practice, 13(60),1-24 [https://doi.org/10.1007/s42519-019-0064-5]

See Also

checkStarIsomorphism for checking the isomorphism of stars. checkSpreadEquivalence for checking the equivalence of spreads.

Examples

# NOT RUN {
## Example 1: two non-equivalent stars of PG(4,2)
data(starn5t3a)
data(starn5t3b)

# test their equivalence
(test1 <- checkStarEquivalence(starn5t3a, starn5t3b))





## Example 2: two equivalent stars of PG(7,2) consisting of 6-flats
data(starn8t5a)

#permute the flats and flat order of starn8t5a to create a second equivalent spread equiv_starn8t5a.
equiv_starn8t5a <- starn8t5a
dims <- dim(equiv_starn8t5a)
for(i in 1:(dims[3])){
   equiv_starn8t5a[,,i] <- equiv_starn8t5a[,sample(1:dims[2], dims[2]),i]
}
equiv_starn8t5a <- starn8t5a[,,sample(1:dims[3], dims[3])]

(test2 <- checkStarEquivalence(starn8t5a, equiv_starn8t5a))
# }