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## Re: [Help-gsl] Constraints for B-spline breakpoints

**From**: |
Rhys Ulerich |

**Subject**: |
Re: [Help-gsl] Constraints for B-spline breakpoints |

**Date**: |
Tue, 13 Oct 2009 07:47:48 -0500 |

>* I'm using the GSL B-spline functions to implement cubic spline smoothing.*
>* My program is based on the example in the manual*
>* (http://www.gnu.org/software/gsl/manual/html_node/Example-programs-for-B_002dsplines.html).*
>
>* I want to allow varying numbers of breakpoints (nbreak) to achieve different*
>* degrees of smoothing. The minimum nbreak for cubic splines is 2, but is*
>* there a maximum?*
There should not be from the gsl_bspline routines.
>* If I use more than n-2 (where n is the number of data*
>* points), I get an error from "gsl_multifit_wlinear" when computing the*
>* spline coefficients:*
>* gsl: svd.c:236: ERROR: svd of MxN matrix, M<N, is not implemented*
>
>* For the offending fit matrix, M = n and N = ncoeffs = nbreak+k-2 = nbreak+2.*
I'm not familiar with the svd routine. Someone else will have to jump in here.
>* Is there a way to use every (distinct location of a) data point as a*
>* breakpoint (via "gsl_bspline_knots")?*
Yes, that should be possible if you get past the SVD constraint from above.
In that case you're just fitting a cubic spline interpolant and you may wish
to use http://www.gnu.org/software/gsl/manual/html_node/Interpolation.html
>* Would it be possible to have more breakpoints than data points?*
Probably, if you're working in a least squares sense.
>* If so, would it make any sense to allow this?*
I'm not sure that you'll gain anything.
- Rhys