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Nonlinear least squares data fitting can be performed using Fit Plot.
To create a Fit Plot, select your X and Y columns in Table, then select
Table → Create Fit Plot in main menu, or use the same item in Table context menu, or use
Create Fit Plot button in the toolbar.
'Nonlinear' means here that analytical fitting function depends nonlinearly on varying parameters (fit parameters). Linear fitting is a quite simple method, which is based on solving the system of linear equations. Unlike linear fitting, nonlinear fitting is performed by iterative algorithm which needs the user to set the initial values of fit parameters.
To fit the data, implement these steps:
This manual does not completely cover the complex nonlinear fitting methodology. We recommend you to take a look at this book:
MagicPlot considers fit function as a sum of Fit Curves. Ordinarily in peaks fitting each Fit Curve corresponds to one peak in experimental data. Click the
Add button to add new Fit Curve to the list. There is a number of predefined Fit Curves types (Line, Parabola, Gauss, Lorentz, etc.) You can also create a Custom Equation Fit Curve and manually enter the formula (Pro edition only). Baseline fitting components may be added to the fitting sum, too.
Fit Plot window contains the list of Fit Curves. Each Fit Curve in the list has three checkboxes:
Show: Specifies whether to show this Fit Curve on plot. Active only if Baseline checkbox is not set
Baseline: Toggles the subtracting of this Fit Curve from experimental data. You also can use
Residualbutton to subtract all Fit Sum from data
Sum: Specifies whether to use this Fit Curve in sum fit function
Below the Fit Curves list is a parameters table which shows names, values, and descriptions of parameters relating to selected Fit Curve.
You can copy and paste Fit Curves from one Fit Plot to another Fit Plot or Figure. You can also paste the copied Fit Curves to the same Fit Plot to create a copy.
Nonlinear fitting assumes that certain initial values of parameters are set before fitting. This procedure is very easy if you use Fit Curves of predefined types (not custom equation): you can drag curves on plot. Initial parameters values for each Fit Curve can also be set in parameter table.
You can adjust Parameters using mouse wheel (scrolling): Hold Ctrl (Cmd on Mac) key and scroll. If Shift key is also pressed the step will be increased.
You can lock parameter(s) to prevent varying this parameter during fit and to prevent its changing due to setting initial values by mouse dragging (for built-in functions). Set the checkbox in
Lock column in parameters list to lock parameter.
You can set the x intervals of the data. Data points outside these intervals are not used to compute the minimizing residual sum of squares (see below). You can use this feature if some data points (especially in the beginning or the end) are inaccurate, e.g. noisy.
Fit Interval tab to set intervals visually or edit accurate borders values:
Fit Interval is also usable when baseline fitting. Before baseline fitting you can specify the interval which does not contain any signal points and contains baseline only. Set
Baseline checkboxes at baseline Fit Curves after baseline fitting to subtract baseline from data. Then specify the whole interval and fit the data.
The most appropriate curve type for baseline fitting is spline.
Note that if you execute one of data processing algorithms (integration, FFT, etc.) on Fit Plot, then the difference between the data and baseline curves (which you do see on the plot) will be processed. You can use this behaviour to exclude baseline from data before integrating, see Integration for more information.
The 'Data-Baseline' column is appended to the Table with initial (x, y) fit data when you create Fit Plot. The 'Data-Baseline' column contains the difference between initial y data and baseline approximation (the sum of Fit Curves for which
Baseline checkbox is set).
It is 'Data-Baseline' column that is actually plotted on Fit Plot.
Use 'Data-Baseline' column in Table if you want to process the data without baseline. This column is also used as initial data if you use
Processing menu when Fit Plot is active.
MagicPlot offers two different ways to view the difference between data and Fit Sum function:
Baselinecheckboxes for all fit function components to subtract them from data and explore the residual plot
Residualbutton. The difference between data and Fit Sum function is shown while button is pressed. You can use either mouse or space key (if button is selected) to hold
You can also use MagicPlot to fit the data with single selected Fit Curve by pressing
Fit One Curve button. In this case a specific data interval for each Fit Curve is used and the main fitting data interval (set in
Fit Interval tab) is ignored. Select
Set Interval checkbox in the bottom of the Fit Plot panel to set specific fit intervals for each Fit Curve.
Because of using individual data interval this method is useful for baseline fitting. In order to fit baseline specify the intervals which does not contain signal (peaks) and contain only noise.
MagicPlot allows coupling of fit parameters. See Joining the Parameters of Fit Curves for details.
MagicPlot indicates fit process with a special window. Fitting curves are periodically updated on plot while fitting so you can see how fit converges.
MagicPlot shows current iteration number and deviation decrement with two progress bars while fit is performed. The fit process stops when one of these progress bars reaches the end.
You can see two buttons on fit progress window:
Break Iterations: Breaks iterations after current iteration. Use this button if you suspect that further iterations will not change the result.
Undo Fit: Breaks iterations and reverts fit parameters to their initial (before fit) values. Use this button if you see that fit process converges to wrong result; change initial values of parameters and run fit again.
You can undo fit and undo changing initial parameters as usual using
Undo function. It is a handy feature when experimenting with different models and initial parameters.