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## Re: [Help-gsl] Multidimensional least-square-fit sought

 From: Patrick Alken Subject: Re: [Help-gsl] Multidimensional least-square-fit sought Date: Thu, 09 Jan 2014 11:06:50 -0700 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:24.0) Gecko/20100101 Thunderbird/24.2.0

On 01/09/2014 10:45 AM, Matthias Sitte wrote:


On 01/09/2014 11:22 AM, Patrick Alken wrote:

You'll want to use the gsl_multifit_linear or gsl_multifit_robust
routines in Least Squares -> multi parameter fitting part of the manual.

You need to build the least squares matrix manually and then pass it to
those routines.

Ok, so solve y = X.c I use c=(c00, c10, c01, c20, c11, c02) and for each
data point (px,py,pz) I add a line to the matrix X with (1, px, py,
px*px, px*py, py*py) and a line the vector y with value pz, right?

Finally, I end up with a linear matrix-vector equation, where y has
(possibly) large number N of rows, X is an N-by-6 matrix, and the result
is a coefficient vector of length 6, right? Plus I get the 6-by-6
covariance matrix and the chi^2.

If so, that's way easier than I thought, but it's GSL 8-) Nice interface!

Thx!
Matthias



Yes that's correct. If you have a lot of noise/outliers in your dataset try the robust fitting routine, otherwise the linear/ordinary least squares routine will work fine.




On 01/09/2014 10:15 AM, Matthias Sitte wrote:

Hi,

I'm looking for a way to to a least-square-fit to a data set (x,y,z).
The fit function should be a polynomal like the following:

z(x,y) = \sum_{m,n=0,m+n<=N}^{N} c_{mn} x^m y^n
= c_{00} + c_{10} x + c_{01} y
+ c_{20} x^2 + c_{11} xy + c_{02} y^2 + ...

I've been using GSL a lot and know my way around, but I don't know the
terminology of least-square-fits, so I'm kindly asking you to name the
proper function(s) I should use before I lose myself in the docs ;-)

Thx,
Matthias