Re: Fitting Gaussians

On Fri, Mar 16, 2001 at 14:51 -0500, Andy Young wrote:
> I'm trying to model emission lines in a CCD spectrum by adding
> Gaussians to the continuum model. The problem I have is that when I
> try to fit the data with the line energy a free parameter I get the
> following error message:
>
> Current parameter values and their derivatives yielded a singular
> matrix
> Chi-square minimization failed
>
> Does anyone have any idea at to what may be causing this and how to
> get around it? A similar procedure works OK in XSPEC (but that can't
> take into account the pile-up in our data)

Hi Andy,

The singular matrix referred to is the matrix of derivatives of
chi^2 w/ respect to each of the variable fit parameters. This
matrix becomes singular when the fit-statistic is nearly
independent of the value of one or more fit parameters. This can
happen when the initial parameter values are far from the best fit
or when the data doesn't constrain one or more parameters.

You might try starting with different initial values or freezing
one or more fit parameters until the parameter space is better
mapped out.

The ISIS 'randomize' function may be helpful for mapping out the
parameter space. When using 'randomize', its a good idea to supply
reasonable min/max values for all free parameters. If min/max
are both zero, the parameter is considered to be unconstrained and
'randomize' will select a random value in the range -DBL_MAX to
+DBL_MAX -- that may not be what you want.

John

--
John C. Houck    MIT Center for Space Research
617-253-3849     One Hampshire St, NE80-6005, Cambridge, MA 02139
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