Re: [PATCH] Add Greville abscissae functionality to B-splines

[Rhys Ulerich <rhys.ulerich@gmail.com>]

Hi Patrick,

I'm fine if you'd like to back out the previous patch until you can
review the two applied together.

The trap I fell into is that, confusingly, the indexing of the
abscissa as it usually appears excludes the very first and very last
knots in GSL's w->knots vector.  Apparently this is a common
convention I didn't know about until I ran into a friend in the hall
today.  Also, the abscissa location should be averaged over degree
(w->km1) knots and not order (w->k) knots.

> I also found a matlab code on it which I used to verify some of your
> test cases, which did look correct.

Odds are good that you can get the new unit tests will also look okay
against that same Matlab code if you (a) throw out the first and last
knot, and (b) use the degree and not the order.

The new patch's documentation includes a reference to a 2005 paper by
Johnson that gives both a definition and an example set of
knots/abscissae for a C3 quartic (Figure 2) if you'd like another
comparison point.

Have a good trip,
Rhys