multimin convergence problem

[Roland Roberts <roland at astrofoto dot org>]

I have a model function which I am trying to an ideal curve.  The
problem stems from building a "barndoor tracker", see
http://hometown.aol.com/davetrott/page17.htm for details on what this
is.

The ideal function is just

    phi(T) = K T

where K = 86400 * 180 / M_PI to measure the angle phi in arcseconds.

The model function is

    L = R T
    theta = 2 arcsin (2 L / r)
    phi = theta + arcsin(sin(theta) / beta)

where R is a fixed parameter (set at R=1/1200) and (r,beta) are the
variables on which the minimization operates.  T is in the range
0--7200 seconds.

What I'm finding is that the ability to get a solution at all is very
sensitive to how I initialize the line search parameters.  The setting
of TOL can vary a lot, but the value of STEP has to fall in a fairly
narrow range or GSL starts spitting out NaNs.  What is frustrating is
that neither the function nor the derivative is returning NaN at any
point; I've verified this by printout out all the function
evaluations.

Is there some magic to picking a good value for STEP?  Shouldn't GSL
return an error rather than setting all my parameters to NaN?  (BTW,
this doesn't seem to matter which solver i pick).

roland
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