Re: fitting, step

On Thu, Jul 08, 2010 at 03:01 -0400, Michael Nowak wrote:
>
> On Jul 7, 2010, at 9:22 PM, John Houck wrote:
>
> >> So now my question is: suppose I really want to do a fit with the
> >> original parameter constraints. Do I need to use subplex? Is there a way
> >> to make mpfit work?
> >
> > mpfit can be made to work in this situation, but I first need to
> > modify the isis fit method interface to provide some additional
>
> Is there a known reason why the narrow constraints fail in this case?

Part of the Levenberg Marquardt method requires computation of
numerical derivatives of the chi-square function with respect
to each fit parameter.  The numerical derivative computation
requires defining a parameter step size. For most parameters,
mpfit currently tries a parameter step size of 1% the parameter
value.

In the example Maurice gave:
   set_par ("egauss(1).center", 3.0325, 0, 3.03, 3.035);
the parameter's full min/max range is only 0.16% of the
parameter's value:
   (3.035-3.03)/3.0325 = 0.0016488
so mpfit's numerical derivative step is much larger than entire
allowed parameter range.

> What exactly are you going to change that will allow this to work?

I'm planning to make the default step smaller and also change
the interface so that one can specify the numerical derivative
step using either an absolute or a relative step size.

In retrospect, it seems rather obvious that 1% is too large for
the default step size because line centers in grating
observations are measured much more accurately than that.

> Just curious, since in using ISIS here in he summer school for
> high res spectra, I've noticed that mpfit *can* be a little
> fussy on narrow lines, unless one runs conf_loops and forces
> fits to find new, lower chi^2, and/or uses subplex.  Either
> makes Monte Carlo simulations of line significances a little
> slower.
>

I hope this change will solve that problem.

Thanks,
-John
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