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## Re: [Help-gsl] Question on Bsplines knot multiplicity

 From: Foivos Diakogiannis Subject: Re: [Help-gsl] Question on Bsplines knot multiplicity Date: Wed, 9 Jul 2014 21:59:46 +0800

```Hi Rhys and all,

Rhys thank you very much for your reply. Just to clarify: with the word
"breakpoints" I mean the vector we feed into gsl routines
to create the knot sequence (which by default has multiplicity of order
equal to the order of the Bspline basis in the end points). So, by
breakpoints I am referring to the knot sequence excluding the multiple
first and last knots.

e.g. say we have a Bspline basis of order k=4 (cubic polynomial), then for
the knot sequence:

{u0,u0,u0,u0,u1,u2,u3,u3,u3,u3},

the breakpoints vector according to the definition above is:

{u0,u1,u2,u3},  with u0<= u1<=u2<=u3.

In tests I am performing today, where I had a vector of breakpoints with
some points (internal knots) of multiplicity less than the order of the
Bspline, everything worked fine. I have not cross checked this with other
software and did not perform extensive tests, however the results seemed
absolutely reasonable. Will perform these kind of tests in the immediate
future and communicate results.

Again, thank you very much for the help and for implementing the Bspline
routines in GSL . You saved me months of work!!!

All the best,
Foivos

On Wed, Jul 9, 2014 at 9:41 PM, Rhys Ulerich <address@hidden> wrote:

> > But
> > I'd suspect there may be edge cases in the code because, as far as I
> > know, they were intended for "breakpoints" and not more general
> > "knots".
>
> To clarify, by "they" I mean "the GSL B-spline implementation"
>
> - Rhys
>

```