[Ifeffit] Purple & Red E Derivatives

[Bruce Ravel]

On Tuesday, February 22, 2011 06:19:16 pm Matthew Marcus wrote:
> > 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

Well ... red pill or purple pill.  They both have side effects that 4
out of 5 doctors advise against :)

So, I do what's easy using Ifeffit as Ifeffit is implemented.  I would
have to code dive (or ask Matt) what the deriv() function actually
does.

A big gap in the data might result in a weird derivative spectrum, but
changes in step size isn't so much of a problem because I ask Ifeffit
to compute d(mu)/d(E).

I agree that "smooth then differentiate" is not obviously better than
"differentiate then smooth".  What is certainly wrong is to do this
inconsistently.

B


-- 

 Bruce Ravel  ------------------------------------ bravel at bnl.gov

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