2.3.3.3.100. NXfit¶
Status:
base class (contribution), extends NXprocess
Description:
Description of a fit procedure using a scalar valued global function
Symbols:
The symbols used in the schema to specify e.g. dimensions of arrays.
dimRank: Rank of the dependent and independent data arrays (for multivariate scalar-valued fit.)
- Groups cited:
Structure:
label: (optional) NX_CHAR
Human-readable label for this fit procedure.
figure_of_meritMETRIC: (optional) NX_NUMBER {units=NX_UNITLESS}
Figure-of-merit to determine the goodness of fit, i.e., how well the fit model ...
Figure-of-merit to determine the goodness of fit, i.e., how well the fit model (i.e., the set of peaks and backgrounds) fits the measured observations.
This value (which is a single number) is often used to guide adjustments to the fitting parameters in the peak fitting process.
@metric: (optional) NX_CHAR
Metric used to determine the goodness of fit. Examples include: ...
Metric used to determine the goodness of fit. Examples include:
\(\chi^2\), the squared sum of the sigma-weighted residuals
reduced \(\chi^2\):, \(\chi^2\): per degree of freedom
\(R^2\), the coefficient of determination
Data and results of the fit.
input_independent: (optional) NX_NUMBER (Rank: dimRank) {units=NX_ANY}
Independent variable(s) for this fit procedure, representing the values to b ...
Independent variable(s) for this fit procedure, representing the values to be fitted by the
global_fit_function.input_dependent: (optional) NX_NUMBER (Rank: dimRank) {units=NX_ANY}
Dependent variable(s) for this fit procedure (i.e., the observed data).
fit_sum: (optional) NX_NUMBER (Rank: dimRank) {units=NX_ANY}
Resulting fit obtained by evaluating the ``global_fit_function`` at the poin ...
Resulting fit obtained by evaluating the
global_fit_functionat the points specified ininput_independentusing the optimized fit parameters. This represents the best-fit curve or surface approximating the input_dependent data.residual: (optional) NX_NUMBER (Rank: dimRank) {units=NX_ANY}
The difference between the observed data (``input_dependent``) and the predi ...
The difference between the observed data (
input_dependent) and the predicted fit values (fit_sum). A lower magnitude of residuals indicates a better fit.peakPEAK: (optional) NXpeak
An instance of the peak model. ...
An instance of the peak model. If there is no characteristic name for each peak component, the peaks could be labeled as peak_0, peak_1, and so on.
total_area: (optional) NX_NUMBER {units=NX_ANY} ⤆
Total area under the curve (can also be used for the total area minus any ...
Total area under the curve (can also be used for the total area minus any background values).
relative_sensitivity_factor: (optional) NX_NUMBER {units=NX_UNITLESS}
Relative sensitivity for this peak, to be used for quantification in ...
Relative sensitivity for this peak, to be used for quantification in an NXprocess.
As an example, in X-ray spectroscopy could depend on the energy scale (see position), the ionization cross section, and the element probed.
relative_area: (optional) NX_NUMBER {units=NX_ANY}
Relative area of this peak compared to other peaks. ...
Relative area of this peak compared to other peaks.
The relative area can simply be derived by dividing the total_area by the total area of all peaks or by a more complicated method (e.g., by additionally dividing by the relative sensitivity factors). Details shall be given in global_fit_function.
backgroundBACKGROUND: (optional) NXfit_background
One fitted background (functional form, position (see :ref:`data/input_indepen ...
One fitted background (functional form, position (see data/input_independent), and intensities) of the peak fit. If there is no characteristic name for each peak component, it is envisioned that backgrounds are labeled as background_0, background_1, and so on.
global_fit_function: (optional) NXfit_function
Function used to describe the overall fit to the data, taking into account the ...
Function used to describe the overall fit to the data, taking into account the parameters of the individual NXpeak and NXfit_background components.
formula_description: (optional) NX_CHAR ⤆
Often, if the peaks and fit backgrounds are defined independently (i.e, with ...
Often, if the peaks and fit backgrounds are defined independently (i.e, with their own parameter sets), the resulting global fit is a function of the form \(model = peak_1(p_1) + peak2(p_2) + backgr(p_3).\), where each \(p_x\) describes the set of parameters for one peak/background.
error_function: (optional) NXfit_function
Function used to optimize the parameters during peak fitting.
description: (optional) NX_CHAR ⤆
Description of the method used to optimize the parameters during peak fittin ...
Description of the method used to optimize the parameters during peak fitting. Examples:
least squares
non-linear least squares
Levenberg-Marquardt algorithm (damped least-squares)
linear regression
Bayesian linear regression
formula_description: (optional) NX_CHAR ⤆
For the optimization, the formula is any optimization process on the ``globa ...
For the optimization, the formula is any optimization process on the
global_fit_functiongiven above. As an example, for a least squares algorithm on independent components, the formula of theerror_functionwould be \(LLS(peak_1(p_1) + peak_2(p_2) + backgr(p_3))\), where each \(p_i\) describes the set of parameters for one peak/background. In this case, theformula_descriptioncan be expressed as \(min(\chi^2)\), where \(\chi^2\) is the sum of squared residuals between the model and the observed data: \(min(\chi^2) = \sum_{i=1}^{N} \left( y_i - \left( \text{peak}_1(p_1, x_i) + \text{peak}_2(p_2, x_i) + \text{backgr}(p_3, x_i) \right) \right)^2\)It is however also possible to supply more involved formulas (e.g., in the case of constrained fits).
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