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

**Follow-Ups**:**Re: Re: NonlinearFit problem***From:*DrBob <drbob@bigfoot.com>