add cubic spline option

[k-doering-NOAA]

Thanks @iantaylor-NOAA for contributing this idea. cubic spline selectivity functionality would be really helpful (discussed in r4ss/r4ss#63 as well as r4ss/r4ss#48.

[k-doering-NOAA]

I think the definitions for the admb functions are here: http://api.admb-project.org/vcubicspline_8cpp_source.html

I'm curious how they differ from spline interpolations in r, like stats::spline. If they are similar (or even kind of similar) perhaps we could just rely on the R functionality instead of needing to use admb.

[k-doering-NOAA]

@iantaylor-NOAA , do you have any r code that mimics the cubic spline selectivity? We basically just need a function that reads in the params as input and outputs the selectivity patterns to use in the GUI (and hopefully, this need not rely on admb...)

[k-doering-NOAA]

Also, any selectivity functions could be safely added here: https://github.com/r4ss/shiny_selex/blob/main/selex_fxns.R. They will not mess up the Shiny app.

[iantaylor-NOAA]

Thanks for moving this idea forward, @k-doering-NOAA.
When I first worked on setting up a widget for cubic spline selectivity long ago, I was not able to replicate (or even fully understand) the ADMB implementation of the spline function and thus just relied on an ADMB executable to do the calculations.

However, I believe that @roliveros-ramos was able to get a good match as part of his work on empirical selectivity with IATTC (which we really need to finish integrating into r4ss).

@k-doering-NOAA, one of us could compare the results of code here to the results of an Stock Synthesis model with splines:
https://github.com/roliveros-ramos/r4ss.selectivity/blob/master/R/selectivity_pattern-27-splines.R.

[k-doering-NOAA]

Another potential resource is the spline function Neal uses in the GUI: https://github.com/nmfs-stock-synthesis/ssi/blob/master/src/ttk_spline.h

[k-doering-NOAA]

Finally, the actual admb function to get the spline selectivity values is: http://api.admb-project.org/cspline_8cpp_source.html#l00037

(vcubic_spline_function eventually passes to this function)