DM2003 provides several curve fitting tools available in
Process|Fitting submenu, including
Linear, Manual and
NLSF fitters, where NLSF stands for non-linear least-square fitting. DM2003
implements one of the most popular and effective NLSF algorithms, namely
Levenberg-Marquardt algorithm, that can be thought of as a trust-region
modification of the well-known Gauss-Newton algorithm.
First you should plot data to be fitted because this tool works only with
active plot series; then select appropriate menu item to load NLSF Fitter
HTML application into the
Browser window. When source data will be plotted in a new temporary
data window, you are ready to start interactive fitting procedure. It
includes following steps:
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: cx (independent variable), p1, p2...p26.
Then click "Update" button to display parameters table (number of parameters
determined by the expression).
In the parameters table, enter initial values of the fitting parameters.
You may verify parameter values before start fitting session: click "Update"
button to update fit curve and see how fit curve conforms source data. Please 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. Probably you
will have to select parameter values manually before start fitting. 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.
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 are displayed near parameter values. In addition, you may use plot
selector tool to restrict fitting data range. Repeat this step until you get
satisfactory results. If problems persist, try to change fitting options (step 4)
or try another fitting model (step 1).
One good practice is so-called "partial fitting": you fix some parameters and
find others in the region where fixed parameters are not important (using
point selector tool); then release fixed parameters and fix those you just
have found, change fitting area and repeat the procedure.
When you click OK button, you may save fitting results in several ways.
Available options are: copy best fit curve to the new plot series in the source
window, add fitting results to the Notes window
or add parameter set to the selected worksheet.
Additionally, there's a set of options that allows you to have full
control over the fitting process:
Convergence thresholds determine whether fitting iterations should be
stopped if parameters or Chi-square changes between iterations are less then
Maximal number of iterations determines how many Levenberg-Marquardt
iterations will be performed when user clicks "Fit" button
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.
Fitted curve may have weight. When X and Y columns are copied from series
properties, column containing weight data should be selected from this list.
Notice that actual data copying will be performed when user clicks "Fit"
fitter is available via OLE Automation (see
IDMApplication2 interface for more details).
This feature allows you to create powerful automatic routines for initial
parameter evaluation and batch fitting.