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Re: Weighted polyfit?


From: Carlo de Falco
Subject: Re: Weighted polyfit?
Date: Fri, 26 Mar 2010 12:22:47 +0100


On 26 Mar 2010, at 10:36, Matthias Brennwald wrote:

Dear all

I am pretty sure this is something that has been discussed previously, but I was not able to find anything helpful. I'd like to fit a polynomial to my experimental data. The data have errors, and I'd like to use these errors as weights for the data values in the fit. Something like this:

   x     = [0:10];                      % x values of experimental data
   y     = x.^2;                                % y values of experimental data
   y_err = randn(size(x));      % errors of y
[p,s] = polyfit (x,y,2); % <-- replace this by something that takes into account the errors (y_err), e.g. using the weights 1./ y_err for each value in y

Any hints or ideas?

Matthias

Polyfit does not do this but, if your weights are all strictly positive it should be quite easy to modify it. If I am not mistaken (please check I am not completely wrong before actually using this) what you want to do corresponds to applying a diagonal left- preconditioner to the least-square vandermonde system.
i.e. add something like

D = diag (sqrt(weights));
v = D*v;
y = D*y;

at line 87 in polyfit.m
c.


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