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Re: Re: Apparent accuracy error in least squares fit

• To: mathgroup at smc.vnet.net
• Subject: [mg66256] Re: [mg66206] Re: Apparent accuracy error in least squares fit
• From: "Chris Chiasson" <chris at chiasson.name>
• Date: Fri, 5 May 2006 05:03:38 -0400 (EDT)
• References: <e346pr$7rn$1@smc.vnet.net> <e39kgv$cqu$1@smc.vnet.net> <200605040920.FAA09491@smc.vnet.net> <200605041624.38589.daniel.ortega@uca.es>
• Sender: owner-wri-mathgroup at wolfram.com

The code shows I tried with both data sets you gave.
??

On 5/4/06, Daniel Ortega <daniel.ortega at uca.es> wrote:
> Of course, I told you that with this dataset, the program worked. The trouble
> appears when the experimental values are lower; for instance:
>
> {300., 2.7933}, {350., 2.7832}, {400., 2.7452}, {450., 2.6898},
> {500., 2.5623}, {550., 2.3616}, {600., 2.0242}, {650., 1.5675},
> {700.,1.0732}, {740., 0.693}}
>
> Using them, the fitting procedure diverges, throwing the message:
>
> FindRoot::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 merit function. You may need more than
> \
> MachinePrecision digits of working precision to meet these
> tolerances.
>
> Thank you very much Chris.
>
> El Jueves, 4 de Mayo de 2006 11:20, escribió:
> > Here is what I get. There are no error messages.
> >
> > In[1]:=
> > $Version
> > Out[1]=
> > 5.2 for Microsoft Windows (June 20, 2005)
> > In[2]:=
> > f[T_,Ms_]=Ms-Mo*Coth[(a+b*Ms)/T]+Mo*T/(a+b*Ms)
> > Out[2]=
> > \!\(Ms + \(Mo\ T\)\/\(a + b\ Ms\) - Mo\ Coth[\(a + b\ Ms\)\/T]\)
> > In[3]:=
> > data={{300.,2.7933},{350.,2.7832},{400.,2.7452},{450.,2.6898},{500.,
> >
> > 2.5623},{550.,2.3616},{600.,2.0242},{650.,1.5675},{700.,1.0732},{740.,
> >       0.693}}
> > Out[3]=
> > {{300.,2.7933},{350.,2.7832},{400.,2.7452},{450.,2.6898},{500.,2.5623},{550
> >., 2.3616},{600.,2.0242},{650.,1.5675},{700.,1.0732},{740.,0.693}} In[4]:=
> > g=Apply[Plus,Map[Sqrt[f[#[[1]],#[[2]]]^2]&,data]];
> > In[5]:=
> > {sol1,sol2}=NMinimize[{g,0<a,0<b,Mo>0},{a,b,Mo}]
> > Out[5]=
> > {3.41302,{a\[Rule]17.3187,b\[Rule]6.81003,Mo\[Rule]91.5214}}
> > In[6]:=
> > data={{300.,9.4478},{350.,9.1237},{400.,8.6531},{450.,8.0999},{500.,
> >
> > 7.4426},{550.,6.706},{600.,5.8785},{650.,4.9522},{700.,3.8981},{750.,
> >       2.9685}}
> > Out[6]=
> > {{300.,9.4478},{350.,9.1237},{400.,8.6531},{450.,8.0999},{500.,7.4426},{550
> >., 6.706},{600.,5.8785},{650.,4.9522},{700.,3.8981},{750.,2.9685}} In[7]:=
> > g=Apply[Plus,Map[Sqrt[f[#[[1]],#[[2]]]^2]&,data]];
> > In[8]:=
> > {sol1,sol2}=NMinimize[{g,0<a,0<b,Mo>0},{a,b,Mo}]
> > Out[8]=
> > {0.479589,{a\[Rule]0.00152594,b\[Rule]194.249,Mo\[Rule]11.3153}}
>
> --
> Daniel Ortega Ponce
>


--
http://chris.chiasson.name/

• References:
  • Re: Apparent accuracy error in least squares fit
    • From: "Chris Chiasson" <chris.chiasson@gmail.com>