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

[<ln...@dr...>]

> On Tue, 23 Oct 2007 18:05:29 +0200, <ln...@dr...> wrote:
>
>> Concerning the spline differentiating question: I am aware that spline=
s
>> can cause unwanted oscillations,
>
> 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 l=
ead
> to some fairly unexpected and sometimes extreme excursions from the zon=
e
> where the real data lie.
>

I beg to disagree: you certainly are not forced to go through all your da=
ta
points for a smoothed spline. Of course, csplines do this way, but acspli=
nes not
(and bezier curves also do not necessarily pass through all the points).

> Sometimes it's just clearly the wrong way to respresent certain data.
> Sometimes it's less obvious but still wrong, this is more dangerous. Si=
nce
> the constraints on the continuity of the differencial are *completely
> artificially* imposed as being the very definition of the spline fit , =
I
> believe it is utterly wrong to place any scientific meaning on the
> derivative of a spline fit.
>

Did you try acsplines (it seems me what you say applies mostly for csplin=
es)? I
wouldn't say that the differential of such an acspline (if it is carefull=
y
drawn) has no scientific meaning. After all, you certainly remember the t=
ime
there were no personal computers and everybody was forced to draw the cur=
ve
himself for a dataset on a piece of paper then graphically differentiate =
this
curve by placing tangents and calculating their slopes. This is exactly t=
he same
thing I would like to do, but now aided by the computer. (Maybe smoothing=
 is not
the exact term for this, that's why we seem to disagree?) Every measureme=
nt,
fitting, analysing method has its own inaccuracies and problems in the re=
al
world you must be aware of. This applies either to curve fitting or smoot=
hing.
It is only in mathematics where things are clearly defined and rigorous.

> I would invite you to reflect on what that means for your results and
> maybe have a quick look at the maths behind spline fitting to check wha=
t I
> say. The maths is pretty simple actually but it's important to know wha=
t
> you are doing in applying such a fit.
>
> Many people apply even least squares fits to completely inappropriate d=
ata
> because they do not realise the basic assumptions of the maths behind i=
t,
> that is that y errors are >> x errors. If that's not true you get the
> wrong fit!
>
>> but in the past I was succesfully using
>> acsplines with weights carefully chosen to approximate the curve I wou=
ld
>> draw by hand through the experimental data.
>
> Well I certainly hope you're not using that sort of bad science for
> anything more than personal curiosity.
> It does not sound like valid , reproducable scientific analysis. :)
>

I used this method to calculate meaningful results. At least not less mea=
ningful
that I would have obtained by graphical differentiation on a piece of pap=
er.
See: you have a bunch of data points and you simply don't know which is t=
he
mathematical function you should fit them to. You sometimes even don't ex=
actly
know what the exact error on x or y values is, but have only a clue. Don'=
t
misunderstand me: I don't need to have something very precise, only at gi=
ven
extent (certainly more precise than doing a "differentiation" on the poin=
ts
themselves, which have a certain scatter due to imprecisions and perturba=
tions).
By the way, even if I fit a mathematically well-defined function to these=
 data
with the Marquardt-Levenberg method, I am not sure that this is the funct=
ion
which describes most accurately the phenomenon solely because the curve h=
as a
similar shape than the points plotted.

> gnuplot claims not to do data processing (other than fitting user defin=
ed
> functions) although "smoothing" data with splines clearly is just that.
>
> I think you should be looking at applying some recognised data processi=
ng
> techniques to your data rather than hand tweeking splines.
>
> I hope my comments have highlighted some of the traps , in particular w=
ith
> regards to the derivative that you are interested in.
>
> regards, Peter.
>

My biggest problem for the moment is the following: I did not find anythi=
ng
useful about 'assignment' in the help file (I have the most recent CVS ve=
rsion
of gnuplot, of course). How should I use it then? Is there a configure-ti=
me
switch needed to compile it into gnuplot?

Levente