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.
