ConditionallyIndependent_MutualInformation( LGObj,Var1,Var2,ConditionalVar )

function [MI,R,M ] = ConditionallyIndependent_MutualInformation( LGObj,Var1,Var2,ConditionalVar )
% VarData1,VarData2,and ConditionalData must have the same number of rows
% I(VarData1,VarData2|ConditionalData )

if nargin == 3 || isempty( ConditionalVar ) == 1 
    [MI,R,M ] = MarginallyIndependent_MutualInformation( LGObj,Var1,Var2);
    return
end
MI = 0;
LG = struct( LGObj );

    N  = LG.CaseLength;
    OriginalData = LG.VarSample;
    UsedSample = DiscardNoneExist( LG.VarSample,[ Var1,Var2,ConditionalVar ] );
    M = N - sum( UsedSample );

     Range1 = LG.VarRange( Var1,: );
     Dim1 = LG.VarRangeLength( Var1 );
     Range1 = Range1( 1:Dim1 );

     Range2 = LG.VarRange( Var2,: );
     Dim2 = LG.VarRangeLength( Var2 );
     Range2 = Range2( 1:Dim2 );

R =( Dim1 -1 ) * ( Dim2 - 1 );
R = R * prod( LG.VarRange( ConditionalVar ));

% The location of the first unprocessed sample, it accelerates the
% searching. 
  d = 1 ; 
  while d <= N
      Frequency = zeros( Dim1,Dim2 ); 
      while d <= N && UsedSample( d ) == 1  
          d = d + 1;
      end
      if d > N,break;end
      ParentValue = OriginalData( d, ConditionalVar );
      
      for t1 = 1:Dim1
          if Range1( t1 ) == OriginalData( d,Var1 )
              break;
          end
      end
      
      for t2 = 1:Dim2
          if Range2( t2 ) == OriginalData(d, Var2 )
              break;
          end
      end      
      Frequency( t1,t2 ) =  1;
    % VarValue
     UsedSample( d )=1;
     d = d + 1;
     if d > N,break;end
    % test whether the class value in Sample(t) is the same as VarValue or not. 
     for t = d:N
         if UsedSample( t )==0
             if ParentValue == OriginalData( t, ConditionalVar )
                  t1 = find( Range1 == OriginalData( t,Var1 ));
                  t2 = find( Range2 == OriginalData( t,Var2 ));                
                  Frequency(t1,t2) = Frequency(t1,t2) + 1;
                  UsedSample(t) = 1;
                  %Frequency
             end
         end 
     end
     
      %UsedSample
      %Frequency
      %Fu = zeros(Dim1(1),1); Fv = zeros(1,Dim2(1));      
      Fu = sum( Frequency,2 );
      Fv = sum( Frequency,1 );
      Sum= sum(Fu);
     % 1/20 * log2(1*2/1*1);
      
       for u= 1 : Dim1
            for v=1 : Dim2 
                if Frequency(u,v) ~= 0  % it also makes sure  Fu(u)~=0 and Fv(v) ~=0
                    MI = MI + ( Frequency(u,v)/M ) * log2( Frequency(u,v)*Sum / (  Fu(u)*Fv(v) ) );   
                end
            end
       end
      % WI
  end

end