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Re: NonLinearFit



Phil Howe wrote:

> I'm having a problem working with NonLinearFit, and would like some
> advice. To demonstrate the problem, I'll use a very simple expression,
> y==a*x^c +b, where I have assigned a=3, b=7, and c=2.
> 
> This generates a simple data set:
> data=Table[{x, 3*x^2+7 +5*Random[]},{x,0,4,.2}];
> 
> Now I try to use NonLinearFit.  If I specify the value of the exponent,
> "c", the  routine seems to work. If I ask it to find a value of c, it
> chokes, even if I tell it the right answer:
> 
> NonlinearFit[data,a*x^c+b,x, {{c,2},{b,7},{a,3}}];
> 
> NonlinearFit::"badderiv": "The matrix of model derivatives (dimensions
> \!\({3, 21}\)) includes DirectedInfinity in at least one element.  Try
> fitting without data points having indices in the list \!\({1}\)."

The problem is that NonlinearFit computes the model derivatives, i.e.,

In[1]:= D[a*x^c + b, c]
Out[1]=
   c
a x  Log[x]

and, since your data includes 0, when NonlinearFit evaluates this model
derivative at x->0

In[2]:= % /. x -> 0
Out[2]=
 c
0  a (-*)

you get a DirectedInfinity.  If you delete 0 from your data, 

	data=Table[{x, 3*x^2+7 +5*Random[]},{x,0.2,4,.2}];

everything works fine:

Cheers,
	Paul 

____________________________________________________________________ 
Paul Abbott                                   Phone: +61-8-9380-2734
Department of Physics                           Fax: +61-8-9380-1014
The University of Western Australia            Nedlands WA  6907       
mailto:paul@physics.uwa.edu.au  AUSTRALIA                            
http://www.pd.uwa.edu.au/~paul

            God IS a weakly left-handed dice player
____________________________________________________________________



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