Re: fulfill the (cubic) basis splines the partition of unity at all points in [a,b]?

[Rhys Ulerich]

This time remembering to CC the mailing list...

On Tue, Mar 7, 2023, 9:57 PM Rhys Ulerich <rhys.ulerich@gmail.com> wrote:

> On Tue, Mar 7, 2023, 5:11 PM Simon Wiesheier <simon.wiesheier@gmail.com>
> wrote:
>
>> After reading the manual, it is not clear to me how GNU internally
>> constructs the knot vector.
>> There are the functions,
>> gsl_bspline_knots
>> gsl_bspline_knots_uniform,
>> that create the knot vector based on given breakpoints.
>>
>
> I encourage you to initialize a cubic workspace (k=4, pick nbreak) then to
> use gsl_bspline_knots_uniform to have the GSL construct the knot vector for
> you given some [a, b]. You will be able to observe the multiplicity of the
> various knots in the resulting w->knots. The multiplicity is a consequence
> of the chosen k meaning that if you opted for quadratic or quintic k you
> will see a different knot multiplicity. Play around a bit.
>
> You may (or may not) find the routines at
> https://github.com/RhysU/suzerain/blob/master/suzerain/bspline.h to be
> useful worked examples. Those include forming linear combinations of the
> basis.
>
> - Rhys
>
>>