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Re: curve fitting: works badly?
- Subject: Re: curve fitting: works badly?
- From: agraps(at)netcom.com (Amara Graps)
- Date: Wed, 8 Mar 1995 20:44:15 GMT
- Newsgroups: comp.lang.idl-pvwave
- Organization: NETCOM On-line Communication Services (408 261-4700 guest)
- References: <feil.794506741@retina>,<3jg71l$oin@post.gsfc.nasa.gov> <D51xF0.I2q@midway.uchicago.edu> <3jjg6g$156@larry.rice.edu>
- Sender: agraps(at)netcom15.netcom.com
vek@spacsun.rice.edu (Vincent E. Kargatis) writes:
>This is great (really). But has anyone done a (linear) curvefit that
>includes both X and Y errors? A much harder problem, but much more
>realistic (c'mon, the Real World's *fun*)! NUMERICAL RECIPES has one for
>linear fitting (ch. 15.3), but not for non-linear (no surprise, since it's
>probably nigh impossible). I don't suppose anyone has translated the NR
>routine into IDL?
I think the IDL Goddard Astronomy Library has IDL code to do linear
curvefit with x and y errors. See the IDL FAQ for how to get to the
library. I don't have the library information handy (but Bill Thompson
might :) ).
>Also, why does CURVEFIT want weights instead of errors? W = 1/(sig_y)^2.
>Whose datasets give them weights? Mine all give me errors! :-)
Mine too!
Seriously, my understanding of why weights instead of errors
is because:
1) Bevington did it that way.
2) It has a precise mathematical definition that can be implemented
easily in least-squares algorithms.
2) There are several different kinds of errors (i.e. instrumental,
statistical, etc. See Bevington for a good discussion of error analysis).
Speaking of errors, if you have criteria for checking whether a fit is
good, looking at the sigma of the output fit parameters is sometimes
not enough because the parameters are correlated to each other. That's
why I added a covariance output matrix to my version of CURVEFIT that
quantitatively describes the correlated variances between the fit
parameters. See my previous post on the Marquardt-Levenberg thread
here on how to do this.
Amara
--
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Amara Graps email: agraps@netcom.com
Computational Physicist vita: finger agraps@sunshine.arc.nasa.gov
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"Awaken the mind without fixing it anywhere." --Kungo Kyo