Re: Some way to differentiate (1st order derivative)?

[<pl...@pi...>]

On Tue, 23 Oct 2007 22:01:33 +0200, <ln...@dr...> wrote:

>>
>> Yes one of the problems with splines is that the contraints placed on
>> continuity and the fact that it must pass through all data points can  
>> lead
>> to some fairly unexpected and sometimes extreme excursions from the zone
>> where the real data lie.
>>
> I beg to disagree: you certainly are not forced to go through all your  
> data
> points for a smoothed spline. Of course, csplines do this way, but  
> acsplines not
> (and bezier curves also do not necessarily pass through all the points).

You are correct to an extent but acsplines are still basically applying a  
cspline and hence the artificial constraints that are the basis of that  
technique.

Massaging the wieghts to get it to "look better" is adding error to error  
it does not correct the fundemental problem.

For example csplines have problems following rapid changes, ie they dont  
follow and then they tend to overshoot badly. If you use acsplines and  
play with the wieghts around the change you may play down the overshoot by  
reducing the surrounding wieghts. But in doing this you mask the change  
that is real. You are further corrupting the data and masking real  
effects, not improving the fit.

The ability to add a column of weights is valuable but these values should  
have some experimental justification not just be used as arbitary fiddle  
factors. I dont think this approach addresses my critisim of csplines.

It may be that you are trying to clobber some fairly high frequency  
experimental noise on an effect that is fairly smooth in nature. In this  
case, as you point out, fiddling coeffs is a bit like a hand drawn line  
and taking a tangent with a ruler and pencil. If that fits your needs  
you're all set, it's good that you were able to find a solution for the  
derivatives.


I think this case in point highlights a lack in gnuplot's offering in the  
"smoothing" department. I've touched on this before.

csplines are pretty heavy handed when it comes to rounding things off and  
produce some severe artifacts unless the underlying nature of the data is  
itself long smooth curves.

I know Hans-Bernhard is going to cry foul and say that gnuplot should not  
be doing data processing. The fact is it does. The trouble is cspines are  
a bit special and the current offering of csplines or bezier is a bit  
one-sided.

It would be nice to have an alternative that suits other sorts of data.  
Some sort of mean or wieghted mean for example.

regards, Peter.