Re: Weighted polyfit?

[Matthias Brennwald]

On Mar 26, 2010, at 12:22 PM, Carlo de Falco wrote:

> 
> 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.

Dear Carlo

I tried this, and it seems to do what I am looking for.

Thanks
Matthias