lmfit-general Mailing List for lmfit - least squares fitting

> what would be considered a "good" starting value=20
I have no other criterion to offer than common sense & experience: plot yo=
ur
data and your starting curve; if their qualitative features (extreme point=
s,
bending points, asymptotes - just the =BBKurvendiskussion=AB stuff) agree, the=
re
is a good chance that the curve will converge towards the data points

> and how could such a value be generated in a generalized manner
for instance, if you are fitting a Gaussian distribution: determine the
center-of-gravity, the width and the height of the distribution from weigh=
ted
sums over your data points.

> I tried fabs(p[1])
good idea

> and sqr(p[1])
even a better idea, provided you really mean sqr and not sqrt
(but why do you use the ugly pow(..,2.0) if you have a sqr function=3F)

> FitFunction4( double t, double* p)
> {
>=20
> double deltax =3D (t-p[0])*(t-p[0]);
>=20
> double dFWHM =3D dHalbwertsbreite;
>=20
> double omega =3D pow(dFWHM/TWOTIMESROOTLN2 , 2.0);
>=20
> return ( p[1]* exp(-deltax/omega) + p[2] ); // Ansatz =FCber Position Gaus=
s
>=20
> }

why don't you leave your Halbwertsbreite free -> yet another fit parameter=


Hope this helps. Otherwise: you may also hire me for consultancy.
Two hours discussion with a data analysis expert may save you
days of deadlock.

Kind regards, Joachim
=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F=5F
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Dear Joachim,

what would be considered a "good" starting value  - and how could such a
value be generated in a generalized manner ?
At the moment I generate three such values which lie more or less around the
required optimum for a gauss function but the
implementation sometimes seems to generate negative amplitudes for a
function of the form specified below. I plotted the initial
points as well as the fit results and found that the deviation was way too
large - it couldn't possiby have approximated the required
curve in the least squares sense. Is there any way of restricting the search
to positiove amplitudes ? I tried fabs(p[1]) and sqr(p[1])
but that didn't seem to work for my case.


FitFunction4( double t, double* p)
{

double deltax = (t-p[0])*(t-p[0]);

double dFWHM = dHalbwertsbreite;

double omega = pow(dFWHM/TWOTIMESROOTLN2 , 2.0);

return ( p[1]* exp(-deltax/omega) + p[2] ); // Ansatz über Position Gauss

}

Any suggestions ?


Regards,

Nandini



----- Original Message -----
From: "Joachim Wuttke" <wu...@we...>
To: <lmf...@li...>; "Nandini Hengen"
<nh...@he...>
Sent: Thursday, May 18, 2006 8:57 AM
Subject: Re: [Lmfit-general] Fitting Periodic Functions using
Levenberg-Marquardt's method


> Dear Nandini,
>
> there is no reason why a fit function ought to be periodic.
>
> Try to track down your problem to one of the following:
> - bad starting values -> did you visualise the initial function before
starting to fit?
> - overflow or underflow in exp
>
> Good luck, Joachim
> _______________________________________________________________
> SMS schreiben mit WEB.DE FreeMail - einfach, schnell und
> kostenguenstig. Jetzt gleich testen! http://f.web.de/?mc=021192
>

Dear Nandini,

there is no reason why a fit function ought to be periodic. 

Try to track down your problem to one of the following:
- bad starting values -> did you visualise the initial function before starting to fit?
- overflow or underflow in exp

Good luck, Joachim
_______________________________________________________________
SMS schreiben mit WEB.DE FreeMail - einfach, schnell und
kostenguenstig. Jetzt gleich testen! http://f.web.de/?mc=021192

Hi,
   the implementation seems to work for nonlinear functions of the form =
A*sine(B) + C, cosine etc. but fails for functions like exp etc. which =
are nonperiodic. Do the relevant functions have to be specified as =
periodic (repetitive) form to ensure convergence ?

Any help is appreciated.

Regards,
Nandini