Re: How to do a Nonlinear Complex Fit ?
- To: mathgroup at smc.vnet.net
- Subject: [mg22502] Re: How to do a Nonlinear Complex Fit ?
- From: "Kevin J. McCann" <kevin.mccann at jhuapl.edu>
- Date: Sun, 5 Mar 2000 00:24:40 -0500 (EST)
- Organization: Johns Hopkins University Applied Physics Lab, Laurel, MD, USA
- References: <89ibb1$mu4@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Ronald,
Here is a notebook that discusses quantum scattering from a potential well.
The problem is we wish to have the solution to the left of the well be
exp(ikx) + R exp(-ikx) and to the right T exp(ikx). It is easier to assume
a solution exp(ikx) far to the right, then propagate backwards to the left.
The solution will then be A exp(ikx) + B exp(-ikx). If we know A, then we
can divide through by A and get our desired result namely R = B/A and T =
1/A. To get A and B we numerically fit a sample of the eigenfunction to the
left of the well to the functions {exp(ikx),exp(-ikx)}. This takes place at
the call to FixedFit. The Fit routine got broken in version 4, although it
may be fixed by now. You could try Fit in place just to see, the arguments
are the same.
I am also posting this to the ng without attachment.
Kevin
Kevin J. McCann
Johns Hopkins University APL
Johns Hopkins Road
----- Original Message -----
From: Ronald Sastrawan <sastra at fmf.uni-freiburg.de>
To: mathgroup at smc.vnet.net
Subject: [mg22502] Re: How to do a Nonlinear Complex Fit ?
> Hello Kevin,
>
> It would be great to have a look at your notebook. It sounds like the
problem I
> am working on.
> Many thanks in advance. I, too believe that others would be interested in
the
> NB, since it seems like a common problem among physisists. (For example,
fitting
>
> of impedance data, which is closly related to my problem).
>
> Ronald
>
> Kevin J. McCann schrieb:
>
> > How about if I send you a notebook? I have fit a exp(ikx) + b exp(-ikx)
to
> > complex data to determine a and b with Fit[]. I have also just done a
> > straight least squares fit to different complex functions. Fit acutally
just
> > does a least squares fit.
> > Let me know, and I can send the NB later today. I would also post the
fact
> > that I did to the newsgroup in case anyone else is interested.
> >
> > Kevin
> >
> > Kevin J. McCann
> > Johns Hopkins University APL
> >
> > ----- Original Message -----
> > From: Ronald Sastrawan <sastra at fmf.uni-freiburg.de>
To: mathgroup at smc.vnet.net
> > To: Kevin J. McCann <kevin.mccann at jhuapl.edu>
> > Sent: Thursday, March 02, 2000 1:59 PM
> > Subject: [mg22502] Re: How to do a Nonlinear Complex Fit ?
> >
> > > Hello,
> > >
> > > Thanks for your answer, but I still don't quite get it.
> > > How would you use Fit to fit a complex function with two sets of data
(the
> > real
> > > and the imaginary part)?
> > > Could you explain in more detail ?
> > >
> > > Thanks,
> > >
> > > Ronald
> > >
> > >
> > > Kevin J. McCann schrieb:
> > >
> > > > Why not just use Fit? Last time I checked, though, PseudoInverse
didn't
> > work
> > > > properly with complex numbers - I have a fix if you need it. Or you
> > could
> > > > just do a straight LSQ fit.
> > > >
> > > > Kevin
> > > >
> > > > --
> > > >
> > > > Kevin J. McCann
> > > > Johns Hopkins University APL
> > >
> > > --
> > > Ronald Sastrawan
> > >
> > > Freiburg Materials Research Center
> > > Stefan-Meier-Str. 21
> > > D-79104 Freiburg
> > > Germany
> > > Tel: ++49/761/203-4802
> > > FAX: ++49/761/203-4801
> > > EMAIL: sastra at fmf.uni-freiburg.de
> > > http://www.fmf.uni-freiburg.de/~biomed/FSZ/forschung-FSZ.html
> > >
> > >
> > >
>
> --
> Ronald Sastrawan
>
> Freiburg Materials Research Center
> Stefan-Meier-Str. 21
> D-79104 Freiburg
> Germany
> Tel: ++49/761/203-4802
> FAX: ++49/761/203-4801
> EMAIL: sastra at fmf.uni-freiburg.de
> http://www.fmf.uni-freiburg.de/~biomed/FSZ/forschung-FSZ.html
>
>
>