Re: Message using FindFit with LevenbergMarquardt Method

*To*: mathgroup at smc.vnet.net*Subject*: [mg125471] Re: Message using FindFit with LevenbergMarquardt Method*From*: Bob Hanlon <hanlonr357 at gmail.com>*Date*: Thu, 15 Mar 2012 00:27:08 -0500 (EST)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201203140541.AAA25797@smc.vnet.net>

Use Sqrt vice sqrt and e0 must also be listed as a parameter. data = {{0., 0.425}, {60.6, 0.224}, {91.2, 0.1314}, {119.4, 0.0716}, {150., 0.040}, {181.8, 0.0241}}; u = t*(a*Sqrt[e0])/2; x = Tanh[t*(a*Sqrt[e0])/2]; Etac = e0*(1 - x^2) // Simplify; fit = FindFit[data, Etac, {a, e0}, t, Method -> "LevenbergMarquardt"] {a -> -1.9229190688022487*^23, e0 -> 0.42500000000000004} This is a very bad fit. You need to provide starting estimates that are "close" to the actual values. fit = FindFit[data, Etac, {{a, 0.1}, {e0, 1}}, t, Method -> "LevenbergMarquardt"] {a -> -0.0404696, e0 -> 0.420337} Plot[Etac /. fit, {t, 0, 200}, Epilog -> {Red, AbsolutePointSize[4], Point[data]}] Bob Hanlon On Wed, Mar 14, 2012 at 1:41 AM, geraldine oliveux <geraldine.oliveux at free.fr> wrote: > Hello, > > I'm a new user of Mathematica. I'm trying to fit data to a model in > which I have one parameter. I try to determine this parameter by > Levenberg-Marquardt Method. > I wrote the following lines : > data = {{0., 0.425}, {60.6, 0.224}, {91.2, 0.1314}, {119.4, 0.0716}, > {150., 0.040}, {181.8, 0.0241}} > u = t*(a*sqrt[e0])/2 > x = Tanh[t*(a*sqrt[e0])/2] > Etac = e0*(1 - x^2) > fit = FindFit[data, Etac, a, t, Method -> "LevenbergMarquardt"] > > But it gives me the following message : > FindFit::nrlnum: "The function value {0.,-0.224+0.425\ (1. -1.\ > Tanh[Times[<<2>>]]^2),-0.1314+0.425\ (1. -1.\ > Tanh[Times[<<2>>]]^2),-0.0716+0.425\ (1. -1.\ > Tanh[Times[<<2>>]]^2),-0.04+0.425\ (1. -1.\ > Tanh[Times[<<2>>]]^2),-0.0241+0.425\ (1. -1.\ Tanh[Times[<<2>>]]^2)}\ > \n is not a list of real numbers with dimensions {6} at {a} = {1.}. " > > What does it mean ? I think there is something I don't do well, and > that it concerns the data declaration. > Thank you in advance for your help, > Best regards, > G=E9raldine >

**References**:**Message using FindFit with LevenbergMarquardt Method***From:*geraldine oliveux <geraldine.oliveux@free.fr>