MarginallyIndependent_MutualInformation( LGObj, Var1,Var2 )

function [MI,R,N ] = MarginallyIndependent_MutualInformation( LGObj, Var1,Var2 )
% calculate the mutual information between two variables
% Input:Vector VarData1 and VarData2 is the data of X1 and X2. 
% Output: MI is the mutual information.
%         r1 and r2 is the number of different values in VarData1 and
%         VarData2
%         N is the validate samples used

     LG = struct( LGObj );
     
     CaseLength = LG.CaseLength;
     Range1 = LG.VarRange( Var1,: );
     Dim1 = LG.VarRangeLength( Var1 );
     VarData1 = LG.VarSample( :,Var1 );

     Range2 = LG.VarRange( Var2,: );
     Dim2 = LG.VarRangeLength( Var2 );
     VarData2 = LG.VarSample( :,Var2 );
   
  R = ( Dim1 - 1 ) *( Dim2 - 1 );
  Frequency = zeros( Dim1,Dim2 );  
  N = 0;
  for q = 1 : CaseLength     % size(VarData1,1) = size(VarData2,1)  
      t1 = find( Range1( 1:Dim1 ) ==  VarData1( q ) );    
      t2 = find( Range2( 1:Dim2 ) ==  VarData2( q ) );
      if isempty( t1 ) == 0 && isempty( t2 ) == 0  % There is possible that t1 or t2 is empty because of invalid value -1 exits.
          Frequency( t1, t2 ) = Frequency( t1, t2 ) + 1;
         N = N + 1;
      end
  end

%  Frequency
  Frequency = Frequency /N;
  Fu        = sum( Frequency,2 );  % Set dim to 1 to compute the sum of each column, 2 to sum rows, etc.
  Fv        = sum( Frequency,1 );
      
  %Fu
  %Fv
  MI=0;
  for u=1 : Dim1
      for v= 1 : Dim2
          if Frequency( u,v ) ~= 0 
              MI = MI + Frequency(u,v)*log2( Frequency(u,v)/(  Fu(u)*Fv(v) ));   
          end
      end
  end
  
end