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

[Patrick Alken]

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