Re: parameters problem in FindFit

*To*: mathgroup at smc.vnet.net*Subject*: [mg92865] Re: parameters problem in FindFit*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Thu, 16 Oct 2008 05:04:15 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <gd4dl4$bg2$1@smc.vnet.net>

gyzhou at 139.com wrote: > I get a list like this : > lis = {{12.5, 1.146}, {32, 1.145}, {50, > 1.144}, {69, 1.1424}, {84.6, > 1.139}} > My aim is : > FindFit[lis, > a - (b x^2)/(c + x), {{a, 1.14}, {b, 0.0003}, {c, 300}}, x] > As we can see, I want this list to be fitted using parameters a, b, c > around 1.14, 0.0003, 300. However Mathematica gives { b, 10^8} and {c, > 10^14} far from what I expect.I set "MaxIterations" to less times, > but it doesn' t make sense. If you plot your model with the parameters returned by FindFit, you will see that the fit is quite good. OTHO, the choice of 300 for c seems to be a poor choice (except if you have some compelling reason from the physical situation your are modeling). Anyway, try to use different methods as illustrated below and check the result on a graph. In[1]:= lst = {{12.5, 1.146}, {32, 1.145}, {50, 1.144}, {69, 1.1424}, {84.6, 1.139}}; In[2]:= model = a - (b x^2)/(c + x); In[3]:= sol = FindFit[lst, model, {{a, 1.14}, {b, 0.0003}, {c, 300}}, x] Out[3]= {a -> 1.14624, b -> 2.45466*10^8, c -> 2.59133*10^14} In[4]:= solar = FindFit[lst, model, {a, b, c}, x, Method -> #] & /@ {"ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "QuasiNewton"} During evaluation of In[4]:= FindFit::lstol: The line search \ decreased the step size to within tolerance specified by AccuracyGoal \ and PrecisionGoal but was unable to find a sufficient decrease in the \ norm of the residual. You may need more than MachinePrecision digits \ of working precision to meet these tolerances. >> Out[4]= {{a -> 1.14769, b -> 0.0000906534, c -> 1.01529}, {a -> 1.14769, b -> 0.0000906534, c -> 1.01529}, {a -> 1.14624, b -> 1.49101*10^8, c -> 1.57403*10^14}, {a -> 1.14388, b -> 9.6559*10^-6, c -> -37.5354}, {a -> 1.14769, b -> 0.0000906531, c -> 1.01317}} In[5]:= Plot[{model /. sol, model /. solar[[1]], model /. {a -> 1.14, b -> 0.0003, c -> 300}}, {x, 10, 100}, Epilog -> Point /@ lst] In[6]:= sol = FindFit[lst, model, {{a, 1.14}, {b, 0.0003}, {c, 300}}, x, Method -> #] & /@ {"ConjugateGradient", "Gradient", "LevenbergMarquardt", "Newton", "QuasiNewton"} During evaluation of In[6]:= FindFit::lstol: The line search \ decreased the step size to within tolerance specified by AccuracyGoal \ and PrecisionGoal but was unable to find a sufficient decrease in the \ norm of the residual. You may need more than MachinePrecision digits \ of working precision to meet these tolerances. >> During evaluation of In[6]:= FindFit::lstol: The line search \ decreased the step size to within tolerance specified by AccuracyGoal \ and PrecisionGoal but was unable to find a sufficient decrease in the \ norm of the residual. You may need more than MachinePrecision digits \ of working precision to meet these tolerances. >> During evaluation of In[6]:= FindFit::lstol: The line search \ decreased the step size to within tolerance specified by AccuracyGoal \ and PrecisionGoal but was unable to find a sufficient decrease in the \ norm of the residual. You may need more than MachinePrecision digits \ of working precision to meet these tolerances. >> During evaluation of In[6]:= General::stop: Further output of \ FindFit::lstol will be suppressed during this calculation. >> Out[6]= {{a -> 1.14637, b -> 0.000365391, c -> 300.}, {a -> 1.14637, b -> 0.000365391, c -> 300.}, {a -> 1.14624, b -> 2.45466*10^8, c -> 2.59133*10^14}, {a -> 1.14624, b -> 4.13776, c -> 4.36807*10^6}, {a -> 1.14637, b -> 0.000365391, c -> 300.}} HTH, -- Jean-Marc