The Fit Wizard

Select Function Tab

The top of the dialog box is used to select one of the three Categories of functions:

To choose a function, first select a category and then the desired function from the displayed Function list.

If the selected function is from the Built-in category and you wish to perform the fit operation using the selected built-in model, you must check the option Fit using built-in function. This will clear the contents of the edit text pane (see image below) and copy the selected function into it.

If the selected built-in model is one of the following peak shape functions: Gauss, GaussAmp, Lorentz, Peaks, PsdVoigt1 or PsdVoigt2, the Peaks input box becomes available, allowing to choose the number of individual peaks for a multi-peak fit operation.

The Peaks built-in fit model is only available in the Pro edition of QtiPlot. If this fit model is selected the Profiles box becomes visible and can be used to customize the profile of each peak, making possible to perform a multi-peak fit with mixed peak profiles.

When the selected built-in model is the Polynomial function the Polynomial order input box becomes available, allowing to choose the order of the polynomial fit function.

If you wish to define your own fit model, the Fit using built-in function option should be unchecked. In this case you can also click the Add expression button to copy the selected function at the current cursor position. If you've selected one of the Basic functions, there are no checkboxes/options available and you need to use the Add expression button.

The bottom half of the dialog box allows to define your own fit models. You can either write your own mathematical expressions from scratch or add expressions from the function selector with the help of the Σ button. When pressing this button a menu pops-up listing all basic mathematical functions provided by QtiPlot. Selecting one of the actions from this menu copies the displayed function into the edit box at the position of the text cursor. Clicking the Clear button removes the contents of the function definition text box.

It is worth mentioning that it is possible to write the name of a basic mathematical function or of a built-in/user defined fit model in the editing panel and after the first two characters QtiPlot pops-up a case sensitive selection list for a faster editing process. The names of built-in/user defined fit models are automatically replaced with their analytical expression.

Once a custom expression is completed, clicking on the Save button adds the function to the list of user defined fit models. The text in the Name field is used as the title of the function. A copy of the function is saved on disk with the extension .fit. You can define the folder where .fit files are saved using either the Choose models folder... button (shown only when "User defined" is selected) or by selecting a new folder in the Save file dialog. Functions can be removed from the User Defined list by selecting them and clicking on the Remove button. You will be asked to confirm the deletion.

Fitting Session Tab

In this second step a starting point should be provided for the fit parameters via the Value column of the Parameters table. The initial values of the fit parameters are by default set to 1.0. The built-in fit models provide a guessing mechanism for the initial values of the parameters. These guesses can be displayed by pressing the button.

Boundary constraints can be defined for the fit parameters if the Range box is checked. This shows the From and To columns of the parameters table. It is also possible to keep the value of some parameters constant during the iterative fit process by checking their corresponding box from the Fixed column. If all the boxes from the Fixed column are checked QtiPlot raises an error message informing that there are no free parameters and that the fit operation cannot be performed.

The numerical format used to display the results of the fit operations can be chosen from the Format list box. The value set in the Precision input box has a different meaning depending on the numeric format. The following format and precision options are available:

In the Data Set tab you can choose the input data set(s) and also choose a weighting method for your fit (the default is No weighting). The available weighting methods are:

1. No weighting: all weighting coefficients are set to 1 (w_i = 1).

2. Instrumental: the values of the associated error bars are used as weighting coefficients w_i = 1/er_i², where er_i are the error bar sizes stored in error bar columns. You must add error bars to the analyzed curve before performing the fit.

3. Statistical: the weighting coefficients are calculated as w_i = 1/y_i, where y_i are the y values in the fitted data set.

4. Arbitrary Dataset: allows setting the weighting coefficients using an arbitrary data set w_i = 1/c_i², where c_i are the values in the arbitrary data set. The column used for the weighting must have a number of rows equal to the number of points in the fitted curve.

5. Direct Weighting: allows setting the weighting coefficients using an arbitrary data set w_i = c_i, where c_i are the values in the arbitrary data set. The column used for the weighting must have a number of rows equal to the number of points in the fitted curve.

In the Algorithm tab you can choose the type of solver as well as a maximum number of Iterations and a Tolerance value. The last two parameters are stopping criteria for the iterative fit process.

The available algorithms are: Scaled Levenberg-Marquardt (obsolete), Unscaled Levenberg-Marquardt (obsolete), Nelder-Mead simplex and Levenberg-Marquardt (MPFIT). The first two algorithms are obsolete and will be removed in a future release of QtiPlot. The Levenberg-Marquardt (MPFIT) algorithm is provided by the MPFIT library. It is the default solver, since it allows defining constant fit parameters for the built-in fit functions. It also handles better the boundary constraints for the fit parameters. In exchange, it cannot be used with plugin fit models. Therefore, the support for plugin fit models will be also dropped, simultaneously with the obsolete fit algorithms.

It is possible to specify how the fit operation responds to modifications of the source data curve using the Recalculate list box. The available options are:

The recalculation mode can be changed later on via the Analysis tab of the plot details dialog.

Custom Output Tab

Depending on the settings in the Custom Output tab, a function curve (option Uniform X Function) or a new table (if you choose the option Same X as Fitting Data) will be created for each fit. The new table includes all the X and Y values used to compute and to plot the fitted function and is hidden by default. It can be found in and viewed from the project explorer.

After the fit, if the Write Parameters to Result Log box from the Options group is checked, the log window is opened to show the results of the fitting process.

The options in the Curves group box can be used to specify if some additional plot curves should be generated after each fit operation. If the Conf. Bands and Pred. Bands options are checked QtiPlot generates confidence bands and prediction bands for the current fit, based on the user defined value for the confidence level. If the Residuals Plot option is checked the curve of the fit residuals is also displayed. The residuals are calculated as the difference between the experimental Y_i values and the response values predicted by the fit model.

The controls in the Parameters Output group box can be used in order to define the options for the display of the results from data fit operations.