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Re: NonlinearFit of an "implicit" function

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94383] Re: NonlinearFit of an "implicit" function
  • From: dh <dh at metrohm.com>
  • Date: Thu, 11 Dec 2008 07:26:37 -0500 (EST)
  • References: <gho399$77$1@smc.vnet.net>


Hi Kretch,

if I understand correctly, you have numerical values for x,y,z,f[x,y,z], 

but symbolically, you have f only implicitely?

Under this assumtptions, you may write the implicite expression in the 

form: G[x,y,z,f]==0.

Using the numerical values for f you can get numerical values for G. 

With this you create data tuples: {x,y,z,G}. Against these, you can fit 

(e.g. using Fit) the symbolllical expression G[x,y,z,ff] where ff is an 

Ansatz  for f.

hope this helps, Daniel



kretch wrote:

> Hi All

> I need to perform a non linear fit of a function which is not provided

> directly i.e. instead of the function having the explicit form

> f(x,y,z) = ...

> I have an implicit  form

> 1/(f(x,y,z) + x^2)^3 = ...

> 

> Now, I know I can manipulate the function so that I get an explicit

> form, but since I have a variety of functions (>100), this would be

> very tedious and error-prone.

> 

> So my question is this:

> I'd like to get the explicit form of the function by "Solve" ing it,

> then run the fit on the explicit form. But for some reason, the exact

> syntax eludes me and I get error messages.

> 

> Can somebody share an example of fitting an implicit function?

> 

> Thanks

> Kretch

> 

> 




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