applyCollineation {IsoCheck} | R Documentation |
Relabel a Spread or Star with a Collineation Matrix
Description
This function relabels a balanced (t-1)-spread or a covering star of
PG(n-1,2)
according to the specified collineation matrix.
Usage
applyCollineation(C, spr)
Arguments
C |
A binary n by n matrix representing a collineation of |
spr |
A balanced spread or star of |
Details
This code applies the relabelling corresponding to a collineation matrix C to any given balanced spread or star of PG(n-1, 2). The spread should be formatted as a 3-dimensional array with spr[i,j,k]
indicating whether or not the i
th basic factor is present in the j
th effect of the k
th flat of spr
. The collineation is applied via a matrix multiplication modulo 2 (i.e., the calculations are done over GF(2)). See Spencer et al. (2019) for details.
Value
A spread or star of the same dimensions as spr.
Author(s)
Neil Spencer, Pritam Ranjan, Franklin Mendivil
References
Spencer, N.A., Ranjan, P., and Mendivil, F., (2019), "Isomorphism Check for 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 balanced spreads.
checkStarIsomorphism
for checking the isomorphism of balanced covering stars.
Examples
## Example 1: relabelling a 1-spread of PG(3,2)
data(spreadn4t2a)
Collin <- cbind(c(1,0,0,1), c(0,0,1,1), c(1,1,1,1), c(0,1,1,1))
# Collin is the collineation matrix corresponding to
# A -> AD, B -> CD, C -> ABCD, D -> BCD
applyCollineation(Collin, spreadn4t2a)
## Example 2: Relabelling a star of PG(4,2) consisting of 4-flats.
data(starn5t3a)
Collin2 <- cbind(c(0,0,0,0,1), c(1,0,0,0,0), c(0,1,0,0,0), c(0,0,0,1,0), c(0,0,1,0,0))
# Collin2 is the collineation matrix corresponding to
# A -> E, B -> A, C -> B, D -> D, E -> C
applyCollineation(Collin2, starn5t3a)