[Ifeffit] Purple & Red E Derivatives

[Matthew Marcus]

> The numerical derivative
> is computed as the numerical differential of the mu(E) spectrum
> divided by the numerical differential of the energy array.  Smoothing
> happens as explained above.  Justw atch the lines that get printed to
> the buffer when you click the plot buttons. - B. Ravel

I wonder if that's the right way to go for data that, for instance, might have gaps or changes in step size.  What I do in my code 
is run a cubic spline through the data, with the abscissa as is,
then take the derivative of that spline.  Thus, if the data is smooth enough to be locally approximated by a cubic, the derivative 
will come out smooth regardless of how it's tabulated.  I'm not
sure that's the case with Bruce's algorithm.  Is the 'numerical differential' the difference E(i+1)-E(i) or (1/2)*(E(i+1)-E(i-1)) or 
some form that's intended to approximate dE(i)/di (i= point index)?

It's not clear to me whether it's any more correct to do smoothing before or after differentiating.  You can take the red pill or 
the blue pill :-)
    mam