PS u0< u1<=u2 <u3. is the correct...
On Wed, Jul 9, 2014 at 9:59 PM, Foivos Diakogiannis < [email protected]> wrote: > 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 <[email protected]> > 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 >> > >
