Description

An abbreviated equivalent is LEV-MAR.

The LEVENBERG-MARQUARDT method is a single-shot method which attempts to find the local fit-statistic minimum nearest to the starting point. Its principal advantage is that it uses information about the first and second derivatives of the fit-statistic as a function of the thawed parameter values to guess the location of the fit-statistic minimum. Thus this method works well (and fast) if the statistic surface is well-behaved. Its principal disadvantages are that it will not work as well with pathological statistic surfaces, and there is no guarantee it will find the global fit-statistic minimum.

The code for this method is derived from the implementation in Bevington (1992).

The eps parameter controls when the optimization will cease; for LEVENBERG-MARQUARDT, this will occur when

| S_i - S_(i-1) | < eps ,

where S_(i-1) and S_i are the observed statistic values for the (i-1)th and ith iteration, respectively.

The smplx parameter controls whether the LEVENBERG-MARQUARDT fit is refined with a SIMPLEX fit. SIMPLEX refinement can be useful for complicated fitting problems where straight LEVENBERG-MARQUARDT does not provide a quick solution. Switchover from LEVENBERG-MARQUARDT to SIMPLEX occurs when delta(S), the change in statistic value from one iteration to the next, is less than LEVENBERG-MARQUARDT.smplxep, for LEVENBERG-MARQUARDT.smplxit iterations in a row. For example, the default is for switchover to occur when delta chi^2 < 1 1 for 3 iterations in a row.