Re: GSoC application review

[Asma Afzal]

Hi Olaf,

>Looking at the documentation of  'nlinfit', I'd guess the returning of 
>additional statistics is the
> reason you chose 'leasqr' to wrap. Is that so?

Yes, precisely. But, I wasn't aware of 'residmin_stat' and
'curvefit_stat' before.

> - one should not be forced to repeat a possibly lengthy optimization
>   to get additional statistics, but be able to just use the result of
>   the optimization for this purpose.

>From what I understand, 'leasqr' needs to be provided with a function
to compute the Jacobian of the residuals.
The default function 'dfdp' computes numerical partial derivatives
with finite differences method.
In [1] you mentioned that the finite differences are handled in a more
sophisticated way in
'nonlin_curvefit/residmin' as a default argument helps identify the
parameter the partial derivative is associated to.
Trying to read through the code, I am assuming that argument is
'hook.plabels'? (Please correct me if I'm wrong).

> This led me to make separate functions for optimization statistics
> (residmin_stat, curvefit_stat). They are frontends, similar to
> nonlin_residmin and nonlin_curvefit, although currently they have only
> backends for weighted least squares.

Nlinfit uses iterative reweighted least squares with different
weighting functions for estimation. A similar function is 'robustfit'
[2]

I started with a small example to see how lsqnonlin, lsqcurvefit and
nlinfit are related:

http://octavegsoc15.blogspot.co.uk/

I think the next step should be to jot down the mapping of all these
functions to Octave's nonlin_residmin, nonlin_curvefit, residmin_stat
and curvefit_stat.

[1] 
http://octave.1599824.n4.nabble.com/Financial-Grid-search-leasqr-to-fit-3-parameters-How-to-speed-up-tp3675973p3709403.html
[2] http://uk.mathworks.com/help/stats/robustfit.html