Path: utzoo!attcan!uunet!cs.utexas.edu!rutgers!sun-barr!decwrl!ucbvax!hplabs!hpl-opus!walker
From: walker@hpl-opus.HP.COM (Rick Walker)
Newsgroups: comp.sources.wanted
Subject: Re: Curve fitting program wanted
Message-ID: <63140006@hpl-opus.HP.COM>
Date: 1 Jul 89 02:58:52 GMT
References: <452@carroll1.UUCP>
Organization: HP Labs, High Speed Electronics Dept., Palo Alto, CA
Lines: 50

/ hpl-opus:comp.sources.wanted / jeff@carroll1.UUCP (Jeff Bartig) /  2:25 pm  Jun 29, 1989 /
> I am looking for a curve fitting program which enables the analysis of
> experimental data using a user defined function.  I would like to be able
> to use it on an IBM PC or a Unix system.  I'm looking for either PD or
> a good commercial package.
> 
> If anyone knows of such a program, please contact me via email.  I will
> mail a summary of what I get to whoever wants one.
> 
> Jeff
> 

Try the Downhill Simplex Method as described on p305-309 in Numerical
Recipes in C, by Press, Flannery, Teukolsky and Vetterling., Cambridge
University Press, 1988.  This is a really neat multi-dimensional
minimizer that is easy to program.  All you need is to do is define a
function y = f(x1,x2,x3...xN, p1, p2, p3, p4...) , where x1,x2... are your
independant variable, and p1,p2... are your adjustable parameters.  Then you
need k experimental data points (in N dimensions):

x11, x12, x13..., x1N,  y1
x21, x22, x23..., x2N,  y2
x31, x32, x33..., x3N,  y3
...
...
xk3, xk2, xk3..., xkN,  yk

Next you define your figure of merit X for your fit to be equal to

X = The SUM from j=1 to j=k of
	[f(xj1, xj2, ... xjN, p1, p2, p3 ...) - yj]^2

This gives a "chi-squared error surface" (equivalent to an RMS figure of merit).

Run the Simplex algorithm on this surface to find a relative minima and you
will have potentially found a good fit for your parameters and your data set.
The routines to do this are alot easier to write than they are to describe.

See the Byte article:

M.S. Caceci and W.P. Cacheris, "Fitting Curves to Data", 1984 BYTE, vol. 9,
no. 5, pp. 340-362.

for a Pascal implementation of the algorithm and a good discussion of the
theory.

It works great!

--------------
Rick Walker,  ...!hplabs!walker