Re: NonlinearFit problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg52055] Re: [mg52033] NonlinearFit problem*From*: DrBob <drbob at bigfoot.com>*Date*: Tue, 9 Nov 2004 01:36:40 -0500 (EST)*References*: <200411080813.DAA07880@smc.vnet.net>*Reply-to*: drbob at bigfoot.com*Sender*: owner-wri-mathgroup at wolfram.com

Here's the Jacobian of f with respect to {a,b}: jac = Outer[D[f, ##1] & , {a, b}, {a, b}] {{(r^a*Log[r]^2)/E^(b*r), (-E^((-b)*r))*r^(1 + a)* Log[r]}, {(-E^((-b)*r))* r^(1 + a)*Log[r], r^(2 + a)/E^(b*r)}} Notice the appearance Log[r], which is undefined for r == 0, which occurs at the first data point. Leaving that point out, we do get a solution: 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}}; f = r^a*Exp[(-b)*r]; NonlinearFit[Rest[data], f, r, {a, b}] r^5.509926608585867/ E^(0.9448215835344381*r) Consider this, too: f /. r -> 0 0^a There's no way to fit that to a y-value, so there's no point in including r = 0 in the data. Bobby On Mon, 8 Nov 2004 03:13:12 -0500 (EST), 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? > > > Feng-Yin Chang, > Institute of Physics,NCTU,Taiwan > > > > -- DrBob at bigfoot.com www.eclecticdreams.net

**References**:**NonlinearFit problem***From:*Feng-Yin Chang <fychang@slac.stanford.edu>