Unlike standard NLSF Fitter Tool, also available via IDMApplication2 interface of DM2003 application objects, Multi-X Fitter Tool uses external DMFitter ActiveX control which may be not installed with DM2003. However, this control allows you to perform NLSF (Levenberg - Marquardt) regression with multidimensional independent variables Y=Y(X1, X2, .. Xn; P1, P2, .. Pm) as shown on the screenshot below:
Nonlinear Levenberg - Marquardt fitter tool in action (click on circle label #2 to display fitting options).
Multi-X NLSF Fitter Tool is a HTML application running in the Browser window. It acts on the active data window and requires sufficient number of lines and columns in the data file displayed by the worksheet viewer. Because it works with multidimensional independent variables while DM2003 graphics engine can display only 2D plots, this fitter doesn't provide visual feedback unlike other fitting tools.
Type desirable fitting expression or select previous input from the drop-down list. This expression must be composed from internal functions (see expression syntax for more details), operators and following parameters: cx1..cx26 (independent variables), p1...p26 (fitting parameters). Then click "Update" button to display parameters table (3) and independent variables combo boxes (4). Numbers of parameters and X vector components are calculated by the expression.
Click Options link in the menu (2) to display Options panel (5) and select additional parameters of the fitting session (this step is optional).
In the parameters table (3), enter initial values of the fitting parameters. Keep in mind that the result of your fitting session critically depends on the initial values of parameters because usually your expression will have a lot of local minima that can prevent fitter to find absolute minimum. You may also fix one or more fitting parameters (by checking appropriate flags), so that their values will not be fitted and remain constant. Parameter deviations will be displayed near parameter values.
Select data columns: for dependent variable you should set Y column in the worksheet viewer as shown on the screenshot, while for components of independent variable (cx1..cx26) you should select appropriate columns using combo boxes (4). When ready, click "Fit" button and wait while fitter finishes calculation (it may take a lot of time for slow computers and long expressions). Fitting progress is displayed in the status line, and the results will be automatically displayed (you can also click appropriate buttons to show fitting results or X columns).
Additionally, there's a set of options (5) that allows you to have full control over the fitting process:
Convergence thresholds determine whether fitting iterations should be stopped if parameters or Chi2 changes between iterations are less then threshold values.
Derivative delta is very important parameter. When you define expression to be fitted as a simple string, NLSF fitter calculates derivatives numerically, by parsing expression string to compute function values and using this parameter as dX. In some cases incorrect values of dX may cause arithmetic overflow or underflow, or another errors. Try to change this parameter if fitter stops work with error messages.
Data points may have weights. Column containing weight data should be selected from this list. Notice that actual data copying will be performed when user clicks "Fit" button.
Maximal number of iterations determines how many Levenberg-Marquardt iterations will be performed when user clicks "Fit" button.
Output options should be used to tell fitter application where it should save fitting results (data file name, parameters, Chi2 and so on). You can add record to the Notes window or add parameter set to the selected data window.
Finally, you should click OK button to save results or Cancel to exit Multi-X NLSF Fitter Tool without saving fitting session.
