Smoothing spline fit
The dialog Smoothing spline fit is used to performa fit of a smoothing spline to a data set. The dialog is opened by selecting from the Edit menu.
In the group Spline the Degree of the spline function as well as the boundaries xmin and xmax of the approximation interval may be set. They give the limits of the range for which the spline can be represented and cover at least the x values of the data set's range selected in the dialog Array. The Smoothing factor affects the averaged deviation of the spline function from the y values of the data set and is equal to the factor, by which the deviations should differ in the average from the error of the data points. A value of 0 leads to a non-smoothing spline.
In the group Data errors the settings for weighing the data points may be formed. The Array for which the settings are performed is shown by its filename and the column indices for x, y, and errors. When the box Error column is checked, the corresponding column of the data set, selected in the dialog Array, is used as the standard deviation of the y values for performing of the fit. Otherwise the standard deviation will be estimated by an error model function taking the x or the y value as its argument. This function and their parameters may be selected in a dialog which is displayed by clicking . A simple error model might be selected by choosing a polynomial with p1 = 0.01, resulting in standard deviations of 1 %.
The fit is performed by clicking the button. The obtained number of knots of the spline, the resulting chi-square value as well as the average deviation of the y values are displayed in the listbox in the lower part of the dialog.
The residuals of the fit (the differences between data and spline function values) can be plotted graphically by use of the button . The plot displayed in a new window then can be printed and saved as a new plot file with the residual data stored internally.
The dialog Roots for finding roots of a cubic spline or of its derivatives is opened by use of the button .
The dialog may be canceled without saving the spline coefficients by use of the button . By using the coefficients are saved and the plot is updated without closing the dialog. With the coefficients are saved and the dialog is closed.