| curve fitting: works badly? [message #3672] |
Mon, 06 March 1995 08:19  |
feil
Messages: 1
Registered: March 1995
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Junior Member |
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I try to use CURVEFIT to get some simple data fitted to an harmonic
oscillator.
Somehow things don't work very good.
these are the datapoints:
i x(i) y(i)
0 8 6.5550 -0.3052
1 8 6.6233 -0.3076
2 8 6.6915 -0.3088
3 8 6.7598 -0.3091
4 8 6.8281 -0.3086
5 8 6.8281 -0.3086
6 8 6.8964 -0.3074
7 8 6.9647 -0.3054
the calling sequence:
;;-------------------- fit to harmonic oscillator ------------------------
a = fltarr(3)
; start estimates
a(0) = etot(icnt/2)
dx = lattice(1)-lattice(0)
a(1) = (etot(2)+etot(0)-2*etot(1))/(dx*dx)
a(2) = lattice(icnt/2)
w = fltarr(icnt)
for i = 0,icnt-1 do begin
w(i) = 1.
end
yfit = mod_curvefit(lattice,etot,w,a)
and the finction itself:
;
; the harmonic oscillator function
;
;
;
pro FUNCT,x,a,f,pder
f = a(0) + a(1)*(x-a(2))^2
PDER = FLTARR(N_ELEMENTS(X),3) ;YES, MAKE ARRAY.
PDER(*,0) = 1.0 ;COMPUTE PARTIALS
PDER(*,1) = (x-a(2))^2
PDER(*,2) = 2*a(1)*(x-a(2))
end
RETURN
end
Simple isn't it.
I never get a decent fit!!!!
HELP HELP
Hans
--
Dr.H.Feil
Philips Research Laboratories, WB-121 | phone : +31-40-742701
Prof. Holstlaan 4 | fax : +31-40-743365
5656 AA Eindhoven, The Netherlands | email : feil@prl.philips.nl
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| Re: curve fitting: works badly? [message #3676 is a reply to message #3672] |
Mon, 06 March 1995 15:49  |
thompson
Messages: 584
Registered: August 1991
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Senior Member |
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feil@prl.philips.nl (Hans Feil) writes:
> I try to use CURVEFIT to get some simple data fitted to an harmonic
> oscillator.
> Somehow things don't work very good.
(stuff deleted)
> pro FUNCT,x,a,f,pder
> f = a(0) + a(1)*(x-a(2))^2
> PDER = FLTARR(N_ELEMENTS(X),3) ;YES, MAKE ARRAY.
>
> PDER(*,0) = 1.0 ;COMPUTE PARTIALS
> PDER(*,1) = (x-a(2))^2
> PDER(*,2) = 2*a(1)*(x-a(2))
^^^^^^^^^^^^^^^
> end
> RETURN
> end
I think that your problem is here. I believe that the sign of this partial
derivative should be negative.
I've often had this problem with this technique. If the partial derivatives
are calculated wrong, you can compute till doomsday and it'll never converge.
I often just don't bother to try to figure it out anymore, and just do the
derivatives numerically.
Bill Thompson
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| Re: curve fitting: works badly? [message #3755 is a reply to message #3672] |
Tue, 14 March 1995 11:16 |
swalton
Messages: 2
Registered: September 1994
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Junior Member |
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I just peeked in here and saw a discussion of one of my recent
favorite topics, nonlinear least squares. (We have IDL, but
I haven't learned it yet; my brain is full :-) ).
I've been using the routine variously known as NL2SOL or N2G. It is
described in ACM Trans. Math. Software, Vol. 9, PP. 369-383 (An
Adaptive Nonlinear Least-Squares Algorithm, By J.E. Dennis, D.M. Gay,
and R.E. Welsch). They are available by anonymous FTP from
netlib.att.com in the freely distributable subset of the AT&T PORT
library. It comes in several versions, including one which can bound
the fit parameters and versions which calculate the derivatives
numerically. The precise details of the algorithm escape me at the
moment, but I'm using it to fit an 11-parameter (!) model to some
solar data. Highly recommended.
As to errors: a recent article in Computers in Physics compared a
couple of different techniques for estimating the errors in a fit, and
concluded that Monte Carlo techniques give the best estimate.
--
Stephen Walton, California State University, Northridge
"Be careful what you wish for; you might get it." swalton@csun.edu
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