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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 22:01:08 +0800

```PS u0< u1<=u2 <u3. is the correct...

On Wed, Jul 9, 2014 at 9:59 PM, Foivos Diakogiannis <

> 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
>>
>
>

```