Re: [PyMca] Documentation for FastXRFLinearFit

[PyMca g. p. m. list. <pym...@li...>]

Thank you so much Armando. This is now crystal clear to me.

Best,
Marc


On Wed, Dec 11, 2019 at 9:38 AM PyMca general purpose mailing list. <
pym...@li...> wrote:

> Dear Marc,
>
> On 11/12/2019 15:36, PyMca general purpose mailing list. wrote:
>
> Dear Armando,
>
> This is a very useful explanation. As I now understand the algorithm, you
> are finding the least-squares solution to the classic Ax=b problem.
>
> Yes, the whole point is that when the A matrix is the same for all the
> spectra, you only need one matrix spectrum.
>
>
> This also seems to be what Chris Ryan and the Geopixie software suite is
> doing with their 'Dynamic Analysis'. I am, however, still confused about
> how the uncertainty weights are applied to the 'Design Matrix'. Is there a
> separate matrix of weights?
>
> An image will help you most.
>
> Take a look at Figure 15.4.1 in Numerical Recipes 2nd or 3rd edition or at
> Figure 14.3.1 in Numerical Recipes 1st edition. Chapter Modeling of data,
> section General Least Squares. If you do not have the book, you can google
> for "numerical recipes pdf" you should find it.
>
> How are these weights predetermined? Is their physical basis really
> counting statistics as you suggest?
>
> Yes. The uncertainty on each point is taken either 1 (no weight),
> sqrt(sum_spectrum)/nspectra (average) or sqrt(ncounts). If you are going to
> use the later, it is better that you use the standard batch in PyMca (it
> will be faster).
>
> As you see in the figure, the uncertainties on the data points enter in
> the A matrix.
>
>
> It would be useful if you could provide a little more mathematical
> description of this aspect of the Fast Linear XRF fit algorithm.
>
> Really, it is just a standard weighted linear fit. Please read the chapter
> mentioned above.
>
> Armando
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