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Fitting with independent parameters

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KolXPD Tutorial - Fitting tutorial

(under construction, version 2011/04/04)

 

This article describes tutorial, which you can download at http://kolxpd.kolibrik.net/ or directly by this link.

 

Au4f (independent parameters)

Select this region, click on FITTING button and explore an example how to fit with independent parameters.

Using add peak button , you can add background and peaks. Parameters of each peak will be added to the table. Peaks are marked by colors both in the table and in the chart.

With add parameter button , you can add a parameter - a number, which can be fitted or calculated by an expression. Parameters can be used in expressions and are useful anywhere, where you need to bind some parameters of peaks by non-constant values, that can be fitted. Independent parameters are added in the table and look like a regular peak with only one parameter. They are referenced in expression in same way - prmX, where X is a number from column P# ("peek number").

Examples of use:

  • If you want more peaks to have the same width, you can add a parameter, set the value and bounds (min, max) and use this parameter in expressions for particular peak parameters. Parameter prm4 is used as gaussian width parameter in this example. Note, that this can be done also without explicit parameters - just set value and bounds of width parameter of first peak and use it in expressions for others. But using an independent parameter is more transparent.
  • If you use independent parameter for binding positions of two peaks, you can define peak distance as an value, that can be fitted in selected range. See the parameter prm5 in this example, which is used to define a distance between two doublets. The value was expected to be around 2 eV, so range of 1.8eV to 2.2eV was defined in min and max columns. Note, that if you want to fit both doublet positions and hold its distance in some bounds, it can not be done without use of an independent parameter.
  • If you want to keep track of some results of fit that must be calculated, it is good idea to add independent parameters and set up its expression accordingly. The value will be updated during fit even if it is not used in fitting.
  • Important usage is for mass-fitting, particularly in huge angle-resolved experiments. If you set up fit function for first spectrum, copy it to all others and start fitting, some fits of thousands of spectra can run out of reasonable bounds. Independent parameters can be used to provide additional weak constrains and improve fitting convergence for cases with imperfect initial conditions.

Notes:

- this describes first version of independent parameters. If someone has comments or ideas, please write me.

- expressions still know only +,-,*,/ operators and don't know operator preference rules and (,). Will improve soon ...

http://kolxpd.kolibrik.net

Last Updated on Wednesday, 22 February 2012 16:23  

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