| Re: solving alghorithm for gaus curves [message #8276 is a reply to message #8223] |
Fri, 21 February 1997 00:00   |
rivers
Messages: 228
Registered: March 1991
|
Senior Member |
|
|
In article <Pine.SUN.3.91.970221120406.3491B-100000@demsyd.syd.dem.csiro.au>, Peter Mason <peterm@demsyd.syd.dem.csiro.au> writes:
> On Tue, 18 Feb 1997, R. Bauer wrote:
>> The next program we want to write will be a flexible fit alghorithm
>> tool.
>> In the first step we want to start with gaussian curves.
>> Is in this group any experience which I can use?
>
>
> Gaussian fitting is a non-linear optimisation problem and can't be done "in one
> go" - e.g., you can't use a (direct) linear least-squares algorithm for the job.
> These non-linear methods are much slower than linear ones because they have to
> iterate towards a solution. What's worse, you usually need to start them off
> reasonably close to the optimal solution, otherwise they can easily converge on
> a non-optimal solution.
>
> My spectra each have hundreds of channels (typically around 600), and I usually
> want to fit 20 to 30 Gaussians to each spectrum. Solving this is very CPU-
> intensive, so I chose to implement the non-linear optimiser in C rather than
> IDL. (An IDL-only version would be far too slow for my particular problem.)
I routinely work on similar scale problems with energy-dispersive x-ray
fluorescence data. There are 2048 channels of data and 10-30 peaks to fit. I
used to use CALL_EXTERNAL to an IMSL fitting routine, but have switched to
using CURVEFIT in IDL. That way the application is portable and an IMSL
license is not required. The performance hit was only about a factor of 2.
Fitting a spectrum on a low-end DEC Alpha takes about 5-10 seconds.
We also fit the background separately.
In general when fitting multiple Gaussians there are 3 parameters to be fit for
each peak: centroid, width and amplitude. In certain applications it may make
sense to constrain one or more of these. For example, when fitting our XRF
data, the position of each peak is typically not optimized, since the
fluorescence energies are known and constant. Rather, only 2 energy calibration
coefficients (which control the relation of channel # to energy) are fitted.
Similarly, I know the instrument response function of my detector is
sigma=A + B*SQRT(energy). Thus sigma of each peak is typically not fitted
independently, but rather only the coefficients A and B are optimized.
Making use of the physics of the experiment not only speeds things up, but
makes for results which are more physically meaningful.
____________________________________________________________
Mark Rivers (773) 702-2279 (office)
CARS (773) 702-9951 (secretary)
Univ. of Chicago (773) 702-5454 (FAX)
5640 S. Ellis Ave. (708) 922-0499 (home)
Chicago, IL 60637 rivers@cars.uchicago.edu (e-mail)
or:
Argonne National Laboratory (630) 252-0422 (office)
Building 434A (630) 252-0405 (lab)
9700 South Cass Avenue (630) 252-1713 (beamline)
Argonne, IL 60439 (630) 252-0443 (FAX)
|
|
|
|
comp.lang.idl-pvwave archive
Members
Search
Help
Login
Home
