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Re: NonlinearModelFit vector valued functions

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  • Subject: [mg120553] Re: NonlinearModelFit vector valued functions
  • From: "Kristof Lebecki" <Kristof.Lebecki at>
  • Date: Fri, 29 Jul 2011 04:40:48 -0400 (EDT)
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Hi everybody,

One year ago following post was placed in this forum (Date: Thu, 4 Feb 2010 06:26:24 -0500 (EST); From: janos). It describes shortly and exactly my problem. Maybe in the last year somebody has found a nice solution?
> NonlinearModelFit is able to fit to a scalar valued function,
> including complex valued functions.
> However, I would like to fit to a vector valued function.
> I can do this using NMinimize,
> but in that case I'll lose all the nice statistics NonlinearModelFit
> provides us.
> Any idea to circumvent this problem?

If you are interested I can describe my problem further, with pleasure ;)
Similarly, as in the case of Janos I use currently FindMinimum. I am happy with it, I use it together with ParallelSum. The only pain are mentioned already missing "nice statistics". 
One option would be to create statistics for FindMinimum. I have read that you can get parameter confidence intervals (mostly interesting for me) when you have Hessian matrix, invert it, etc. Anyhow you will also have to evaluate noise of your data. Shortly speaking: something terribly complex for me.
Other option would be to do some tricks with NonlinearModelFit. If I had 2D real vector function I could for instance transform it into 1D complex function - problem solved. But my function is 3D! I can still imagine other tricks, like mapping N three-dimensional data points into 3N scalar data points. 

But my project is already complex. I have 3D convolutions, my function calculates seconds, so I would prefer "elegant" solution.
So, any help or suggestion is appreciated.
With best regards, Kristof
Kristof M. Lebecki, Dr,
  Fachbereich Physik
  Postfach 674
  Universitat Konstanz
  D-78457 Konstanz, Germany
voice: +49 (0)7531 88 - 3796
  fax: +49 (0)7531 88 - 5325

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