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Re: NonlinearFit problem
*To*: mathgroup at smc.vnet.net
*Subject*: [mg52074] Re: NonlinearFit problem
*From*: Paul Abbott <paul at physics.uwa.edu.au>
*Date*: Tue, 9 Nov 2004 01:37:48 -0500 (EST)
*Organization*: The University of Western Australia
*References*: <cmnabi$7sn$1@smc.vnet.net>
*Sender*: owner-wri-mathgroup at wolfram.com
In article <cmnabi$7sn$1 at smc.vnet.net>,
Feng-Yin Chang <fychang at slac.stanford.edu> wrote:
> Hi All,
> Could anyone give me any suggestion for the specified fitting function
> f= r^a Exp[-b r]?
> My data point was given below,
> data={{0, 1.00002}, {2.31507, 26.4522}, {4.32033, 56.8265}, {6.63539,
> 59.6674}, {8.64066, 39.5536}, {10.9557, 21.6862}, {12.961,
> 10.1456}, {15.276, 4.39652}}
>
> The following way,
> NonlinearFit[data,f,r,{a,b}], gives the error message,
> FindFit::njnum:
> The Jacobian is not a matrix of numbers at (a,b)={1.,1.}.
>
> How should I do this fitting without the problem?
It is the first data point that is causing the problem. As the error
message says, the Jacobian
Outer[D, {r^a Exp[-b r]}, {a, b}]
is not a matrix of numbers at (a,b)={1.,1.}, unless you take the limit
as r->0.
If you drop the first point, or perturb the x value away from 0, the fit
proceeds without problem. For example,
data={{0.0001, 1.00002}, {2.31507, 26.4522}, {4.32033, 56.8265},
{6.63539, 59.6674}, {8.64066, 39.5536}, {10.9557, 21.6862},
{12.961, 10.1456}, {15.276, 4.39652}}
FindFit[data, r^a Exp[-b r], {a,b}, r]
Cheers,
Paul
--
Paul Abbott Phone: +61 8 6488 2734
School of Physics, M013 Fax: +61 8 6488 1014
The University of Western Australia (CRICOS Provider No 00126G)
35 Stirling Highway
Crawley WA 6009 mailto:paul at physics.uwa.edu.au
AUSTRALIA http://physics.uwa.edu.au/~paul
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