> ... 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 _______________________________________________ Help-gsl mailing list Help-gsl@gnu.org http://lists.gnu.org/mailman/listinfo/help-gsl
