Re: [Help-gsl] Bspline fitting

[Rhys Ulerich]

> ... starting from the example given at the end of the chapter on
> Basis Splines of the User Guide. What I did not understand is
> the difference between knots and breakpoints....

Are you referring to the usage of knots from the manual page at [1] ?

   /* use uniform breakpoints on [0, 15] */
   gsl_bspline_knots_uniform(0.0, 15.0, bw);

If so, the definition of both "breakpoints" and "knots" is given at
[2].  For a B-spline basis with the maximum possible continuity (e.g.
k =4 cubic basis in C^2), you can almost think of breakpoints and
knots as the same thing.  The distinction becomes important if you
wanted a basis with either nonuniform or lower continuity (e.g. k = 4
cubic basis in C^1) when repeated knots appear at the breakpoints.

> From a more "practical" point
> of view: what shall I do if I want to divide
> the x axis in --for example-- 3 regions, in
> which the experimental data have to be fitted
> by 3rd order polynomials, and let the x positions
> of the border points of these regions being
> introduced by the user?

Three adjacent regions are determined by four breakpoints.  So use
gsl_bspline_alloc per [3] with k = 4 cubic and nbreak = 4.  Then use
gsl_bspline_knots per [4] where the breakpts parameter is a gsl_vector
of length four containing the four points determining the boundaries
of your three regions.  If, instead, you used
gsl_bspline_knots_uniform per [4] then the three regions would be
uniformly spaced.

- Rhys

[1] 
http://www.gnu.org/software/gsl/manual/html_node/Example-programs-for-B_002dsplines.html
[2] 
http://www.gnu.org/software/gsl/manual/html_node/Overview-of-B_002dsplines.html
[3] 
http://www.gnu.org/software/gsl/manual/html_node/Initializing-the-B_002dsplines-solver.html
[4] 
http://www.gnu.org/software/gsl/manual/html_node/Constructing-the-knots-vector.html