Week3: nlinfit, statset, stat_get and __all_stat_opts__

So this week I achieved the following milestones:

Wrapping nlinfit on nonlin_curvefit

[beta,R,J,CovB,MSE,ErrorModelInfo] = nlinfit(X,Y,modelfun,beta0,options,Name,Value)

Implementation [1]:

I chose not to wrap nlinfit on lsqcurvefit because 

1. We might end up wrapping lsqcurvefit on lsqnonlin eventually so it is undecided.
2. The default options for lsqnonlin/lsqcurvefit are different from nlinfit. 

Missing features:

1. RobustWgtFun - The field RobustWgtFun in options can be provided with a function handle which computes the residuals at every iteration. The backend optimization algorithm in Octave currently does not support this functionality.  
2. Name-Value pairs. Currently the only implemented one is "weights",  which takes an array of weights for the weighted optimization. "ErrorModelInfo" and "ErrorParameters" are not implemented. The possible error models include, "constant", "proportional" and "combined". The error model also translates to a weight function which helps in reducing the effect of outliers.   
3. ErrorModelInfo- output field which gives information about the error variance, and estimates the parameters of Error models. 

Setting options using statset

In Matlab, options for statistics toolbox are set using statset [2].  The functionality is almost identical to optimset but the different functions in Matlab are because of different toolboxes (statset for statistics and optimset for optimization toolbox).

Added functions:

statset.m, statget.m and __all_stat_opts__.m [3]-[5]

Creating these functions was pretty straight forward.

Still to do:

1. Have to check if the weighted residual and weighted Jacobian output in octave is consistent with Matlab and further refine the functions with the feedback from my mentors.
2. Move on to fmincon wrapping nonlin_min.

[1] https://github.com/AsmaAfzal/octave_workspace/blob/master/nlinfit.m
[2] http://uk.mathworks.com/help/stats/statset.html
[3] https://github.com/AsmaAfzal/octave_workspace/blob/master/statset.m
[4] https://github.com/AsmaAfzal/octave_workspace/blob/master/statget.m
[5] https://github.com/AsmaAfzal/octave_workspace/blob/master/__all_stat_opts__.m