EmpiricalSquaredDifference.m

%  sd = EmpiricalSquaredDifference(f1, f2, intBounds)
%  
%  Returns the squared difference of two continuous 
%  functions given by samples and the bounds of the 
%  corresponding intervalls.
%  
%  This function can be used to characterize the distance
%  between two density functions, distribution functions, 
%  etc.
%  
%  Parameters
%  ----------
%  f1 : vector, length M
%      Samples of the first continuous function
%  f2 : vector, length M
%      Samples of the second continuous function
%  intBounds : vector, length M+1
%      The bounds of the intervals. The ith sample
%      corresponds to the interval 
%      (intbounds(i),intbounds(i+1))
%  
%  Returns
%  -------
%  sd : double
%      The squared difference
 
function sd = EmpiricalSquaredDifference (f1, f2, intBounds)
 
    intlens = intBounds(2:end) - intBounds(1:end-1);
    intlens = reshape(intlens, size(f1));
    p1 = f1 .* intlens;
    p2 = f2 .* intlens;
    sd = SquaredDifference (p1, p2);
end