original_matlab_code.m

%create the design matrix, Mi
M = nan(26,3);
Mi = nan(26,6);
Morig = nan(26,3);
i = 1;
unit = [1 0 -1];
for c = unit(1:3)
    for b = unit(1:3)
        for a = unit(1:3)
            M(i,:) = [a b c];
            Morig(i,:) = [a b c];
            if sum(abs(M(i,:)))' == 2
                M(i,:) = M(i,:).*[(1/sqrt(2)) (1/sqrt(2)) (1/sqrt(2))];
            elseif sum(abs(M(i,:)))' == 3
                M(i,:) = M(i,:).*[(1/sqrt(3)) (1/sqrt(3)) (1/sqrt(3))];
            end
            Mi(i,:) = [M(i,1)^2 2*M(i,1)*M(i,2) 2*M(i,1)*M(i,3) M(i,2)^2 2*M(i,2)*M(i,3) M(i,3)^2]; %normalize
            i = i+1;
            [a;b;c];
        end
    end
end

Mi(14,:) = []
Morig(14,:) = []

T = inv(Mi' * Mi) * Mi'