IsoCheck (version 0.1.0)

checkSpreadEquivalence: Checking the Equivalence of Two Spreads

Description

This function checks the equivalence of two (t-1)-spreads of PG(n-1,2) by comparing their sorted bitstring representations.

Usage

checkSpreadEquivalence(spread1, spread2)

Arguments

spread1

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

spread2

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

Value

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

Details

This code checks if two (t-1)-spreads of PG(n-1,2) are equivalent using the bitstring representation of Spencer et al. (2019). Both input spreads should be formatted as 3-dimensional arrays, for example, spread1[i,j,k] indicates 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

checkSpreadIsomorphism for checking the isomorphism of spreads. checkStarEquivalence for checking the equivalence of two stars.

Examples

# NOT RUN {
## Example 1: two non-equivalent 1-spreads of PG(3,2)
data(spreadn4t2a)
data(spreadn4t2b)

# test their equivalence
(test1 <- checkSpreadEquivalence(spreadn4t2a, spreadn4t2b))


# direct instantiation of a spread
spreadn4t2c <- array(NA, c(4,3,5))

spreadn4t2c[,1,1] <- c(0, 0, 0, 1)
spreadn4t2c[,2,1] <- c(0, 1, 1, 0)
spreadn4t2c[,3,1] <- c(0, 1, 1, 1)
spreadn4t2c[,1,2] <- c(0, 0, 1, 0)
spreadn4t2c[,2,2] <- c(1, 1, 0, 0)
spreadn4t2c[,3,2] <- c(1, 1, 1, 0)
spreadn4t2c[,1,3] <- c(0, 1, 0, 0)
spreadn4t2c[,2,3] <- c(1, 0, 1, 1)
spreadn4t2c[,3,3] <- c(1, 1, 1, 1)
spreadn4t2c[,1,4] <- c(1, 0, 0, 0)
spreadn4t2c[,2,4] <- c(0, 1, 0, 1)
spreadn4t2c[,3,4] <- c(1, 1, 0, 1)
spreadn4t2c[,1,5] <- c(0, 0, 1, 1)
spreadn4t2c[,2,5] <- c(1, 0, 1, 0)
spreadn4t2c[,3,5] <- c(1, 0, 0, 1)

(test2 <- checkSpreadEquivalence(spreadn4t2a, spreadn4t2c))





## Example 2: two equivalent 2-spreads of PG(5,2)
data(spreadn6t3a)

# permute the flats and flat order of spreadn6t3a to create a 
# second equivalent spread equiv_spreadn6t3a.

equiv_spreadn6t3a <- spreadn6t3a
dims <- dim(equiv_spreadn6t3a)
for(i in 1:(dims[3])){
   equiv_spreadn6t3a[,,i] <- equiv_spreadn6t3a[,sample(1:dims[2], dims[2]),i]
}
equiv_spreadn6t3a <- equiv_spreadn6t3a[,,sample(1:dims[3], dims[3])]

(test3 <- checkSpreadEquivalence(spreadn6t3a, equiv_spreadn6t3a))
# }