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SOMFIT

This program fits the averaged distances, computed with SOMORJAI, to equation (3.9) and creates plots with the results. Results in this chapter were obtained with a version called SOMFITM, where a Marquardt algorithm (a non-linear least squares method for curve-fitting [Barhorst, 1976]) is used to fit the $\gamma$-weighted distances. The advantage of this procedure, compared to an iterative linear least squares method (in the standard version SOMFIT), is that it returns the variances of the estimated parameters ($D(\gamma)$ and $C$). It requires, however, the derivatives of the function eq. (3.9) with respect to these parameters (see Appendix A). If the correction function cannot be evaluated because of an invalid argument of the gamma function, the nearest neighbour is discarded and the fitting proces repeated. The user should determine the optimal ``fit range'', $[N_{min},N_{max}]$ or $[k_{min},k_{max}]$ by the method of trial and error (bad fit). The program creates a plot of the results and a file with the standard deviations and other (ir)relevant information. The estimation of the entropy function has not been implemented.

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