checkStarEquivalence {IsoCheck}

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).

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.

Value

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

Author(s)

Neil Spencer, Pritam Ranjan, Franklin Mendivil

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

## 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))