Re: [PyMca] Documentation for FastXRFLinearFit

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

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. 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? How are these weights predetermined? Is their physical
basis really counting statistics as you suggest?

It would be useful if you could provide a little more mathematical
description of this aspect of the Fast Linear XRF fit algorithm.

Thanks! And Happy Holidays!

Best,
Marc

On Fri, Dec 6, 2019 at 10:58 AM PyMca general purpose mailing list. <
pym...@li...> wrote:

> Dear Marc,
>
> What follows is a copy-paste of the text from the slides I use for
> training:
>
> """
> As you may have found out with the standard fit, maximum speeds can be
> achieved when you can afford a linear fit:
>
> - Non linear parameters have been previously determined and kept fixed
> - No pile up is considered (remember: pile up is not the same on each
> pixel and average pile up has no meaning
>
> On a linear fit, the signal can be written as a matrix product:
>
> Measured Signal B = Design Matrix * A
>
> In other words, the measured spectrum B is obtained as a linear
> combination of the columns of the Design Matrix and we have to find the
> coefficients A on that basis.
>
> The uncertainties on the measured data enter as weights in the Design
> Matrix that has n_channels rows and m_model_parameters columns.
>
> Therefore, in the linear fit we need the "equivalent of a matrix inversion
> and a matrix multiplication" to obtain the A parameters.
>
> If we assume that the uncertainty associated to the counts in a channel is
> the same on all the measured spectra, the Design Matrix will be the same in
> every point and only one matrix inversion equivalent is needed.
>
> That corresponds to:
>
> - Using No Weight (assume uncertainty is 1 everywhere) or
> - Use an average Weight (derive channel uncertainty from the sum spectrum)
>
> All that is achievable from the GUI or from the command line (no GUI)  in
> source installation of PyMca:
>
> python -m PyMca5.PyMcaPhysics.xrf.FastXRFLinearFit
> --cfg=configuration_file --weight=0 --tif=1 --concentrations=0 --refit=0
> hdf5_file_name::dataset_path
>
> """
>
> Concerning your specific question: The background is accounted for or not
> following what you requested via the fit configuration file. Remember that
> all the non-linear parameters will be fixed to their values in the fit
> configuration file. If they are wrong they will remain wrong. To help on
> that, the fit configuration window allows you to load the parameters of the
> last fit into the configuration ("Load from Fit").
>
> Best regards,
>
> Armando
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