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The Least-Squares Fitting Tool

The least-squares fitting tool provides an automatic method for adjusting the parameters of your model so that it fits the data better. It does this by using a non-linear optimization package to minimize tex2html_wrap_inline1943 for the model and data.

Use the radio buttons at the top left to choose between fitting amplitudes and phases and amplitudes only. The fields at the top are updated during the fitting process and show the number of iterations carried out so far, the number of times that tex2html_wrap_inline1943 has been evaluated (function evaluations) and the current value of tex2html_wrap_inline1943 divided by the number of data points. If the model fits the data within the errors, the last number should be about 1.0.

The large text area at the bottom of the tool is used to report the results of the fit. This shows the conditions under which the fitting process ended and, if successful, the final parameter values and their standard errors (assuming that the data errors have a Gaussian distribution). As is the usual case, these errors represent the standard error in each parameter if only that parameter were in error: in reality, the parameters are not independent of each other and these error estimates will tend to underestimate the actual standard error for any given model parameter.

Start the fitting process by selecting the Fit Data command from the Fitter menu. A dialogue will appear to remind you that the model can not be changed while the fitting tool is working. This dialogue may not appear until the first iteration is complete which make take several minutes. You can use the Cancel button on this dialogue to stop the fitting tool at the earliest possible opportunity.

SLIME is unable to respond to any X events during an iteration of the model-fitting process so it will appear not to be working while an iteraction is being carried out. This may take anywhere from a few seconds to several minutes depending on the complexity of the model and the amout of data you are using. Don't attempt to kill SLIME if it appears to be hang during model fitting: it is still working.

The fitting procedure will report one of several reasons for ending when it has finished.

X-convergence Achieved
The fitting procedure has determined that the parameters lie within the x-convergence tolerance of the parameters which give the minimum value of tex2html_wrap_inline1943 in a scaled parameter space. This is a good result.

Relative function convergence achieved
The fitting procedure has determined that the fractional decrease in tex2html_wrap_inline1943 has dropped below a threshold value and that further significant decreases in tex2html_wrap_inline1943 are unlikely. This is a good result.

Both x-convergence and relative function convergence achieved
Both of the previous conditions ahve been met. This is a good result.

Perfect fit achieved
The fitting tool has found a set of parameter values that fit the data exactly. This is impossible for real data in the absence of a miracle or cheating.

Singular convergence
The data do not constrain one or more parameters of your model. The most frequent problem is that the position angle of a Gaussian component is not constrained by the data (you may see the component rotating in the model editor before this happens). This is a bad result and indicates that you should simplify your model.

False convergence
The fit appears to have converged on a solution that is not a true minimum. In principal these means that the tolerances may be too tight but usually results from using a poor starting model in practice.

Reached an iteration limit
The fitting process either reached the maximum number of iterations or of function evaluations. This usually indicates a poor starting model.

Fitting aborted by user
Self-explanatory.

You can change the convergence tolerances and iteration limits but this is rarely effective and is not recommended.

Irrespective of whether the fit was successful or not, the final parameters will become the current model parameters. If you don't like them for any reason, you can use the Undo function of the model editor to restore the parameters to their pre-fit state.




next up previous contents
Next: The Least-Squares Tool Menus Up: Reference Section Previous: The Phase Range Dialogue

Chris Flatters
Thu Mar 14 16:02:50 MST 1996