function MIhat = MutualInfo(L1,L2)
%   mutual information

%===========    
L1 = L1(:);
L2 = L2(:);
if size(L1) ~= size(L2)
    error('size(L1) must == size(L2)');
end
L1 = L1 - min(L1) + 1;      %   min (L1) <- 1;
L2 = L2 - min(L2) + 1;      %   min (L2) <- 1;
%===========    make bipartition graph  ============
nClass = max(max(L1), max(L2));
G = zeros(nClass);
for i=1:nClass
    for j=1:nClass
        G(i,j) = length(find(L1 == i & L2 == j));
    end
end
sumG = sum(G(:));
%===========    calculate MIhat
P1 = sum(G,2);  P1 = P1/sumG;
P2 = sum(G,1);  P2 = P2/sumG;
H1 = sum(-P1.*log2(P1));
H2 = sum(-P2.*log2(P2));
P12 = G/sumG;
PPP = P12./repmat(P2,nClass,1)./repmat(P1,1,nClass);
PPP(abs(PPP) < 1e-12) = 1;
MI = sum(P12(:) .* log2(PPP(:)));
MIhat = MI / max(H1,H2);
%%%%%%%%%%%%%   why complex ?       %%%%%%%%
MIhat = real(MIhat);