MATLAB script to compute a row-complete Latin square

rowCompleteLatinSquare

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