MATLAB script to compute a row-complete Latin square
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function L = rowCompleteLatinSquare(n) | |
%% ROWCOMPLETELATINSQUARE Compute a row-complete Latin square of order n. | |
% Note: n must be even and greater than zero. | |
% | |
% This function follows | |
% http://personal.maths.surrey.ac.uk/st/H.Bruin/MMath/LatinSquares.html | |
% to which I have been pointed to from | |
% https://math.stackexchange.com/q/991078 | |
% | |
if n<=0 || mod(n,2)~=0 | |
error('n must be even and greater than zero.'); | |
end | |
% create difference vector | |
d = 1:n-1; | |
for i= 2:2:(n-1) | |
d(i)=n-i; | |
end | |
clear i; | |
% preallocate memory | |
L = zeros(n,n); | |
% initialize first column | |
L(:,1) = (0:n-1)'; | |
% populate Latin square | |
for i=2:n | |
L(:,i) = mod(L(:,i-1)-d(i-1),n); | |
end | |
% normalize (match order in first row and first column) | |
L = L(L(1,:)+1,:); | |
% reduce form (remap the symbols so that they are in natural order) | |
L_reduced = zeros(n,n); | |
for i=0:n-1 | |
L_reduced(L==L(i+1,1))=i; | |
end | |
L = L_reduced; | |
clear L_reduced i; | |
end |
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