# Checking the Equivalence of Two Spreads This function checks the equivalence of two `(t-1)`-spreads of `PG(n-1,2)` by comparing their sorted bitstring representations. ```r 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). ## 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 `i`th basic factor is present in the `j`th effect of the `k`th flat of spread1. ## Returns A Boolean indicating whether or not the two spreads are equivalent. ## 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. ## Author(s) Neil Spencer, Pritam Ranjan, Franklin Mendivil ## Examples ```r ## 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)) ```

checkSpreadEquivalence function