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

[Simon Wiesheier]

Is this <https://github.com/ampl/gsl/tree/master/bspline> the relevant
section of the github repository you are referring to?

Am Mi., 8. März 2023 um 06:21 Uhr schrieb Patrick Alken <alken@colorado.edu
>:

> Its also worth mentioning that there has been a substantial overhaul to
> the B-splines routines since v2.7. The new routines are on the git
> repository, along with documentation. If you have the ability to clone
> the git and build the documentation from there I highly encourage it.
> There are many example programs in the git documentation which are not
> in the 2.7 docs which may help you.
>
> On 3/7/23 22:07, Rhys Ulerich wrote:
> > 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
> >>
>
>