38.4 Evaluation of B-splines

Function: int gsl_bspline_eval (const double x, gsl_vector * B, gsl_bspline_workspace * w)

This function evaluates all B-spline basis functions at the position x and stores them in B, so that the ith element of B is B_i(x). B must be of length n = nbreak + k - 2. This value may also be obtained by calling gsl_bspline_ncoeffs. It is far more efficient to compute all of the basis functions at once than to compute them individually, due to the nature of the defining recurrence relation.

Function: int gsl_bspline_eval_nonzero (const double x, gsl_vector * Bk, size_t * istart, size_t * iend, gsl_bspline_workspace * w)

This function evaluates all potentially nonzero B-spline basis functions at the position x and stores them in Bk, so that the ith element of Bk is B_(istart+i)(x). The last element of Bk is B_(iend)(x). Bk must be of length k. Only returning nonzero basis functions allows users to more cheaply perform tasks requiring linear combinations of the basis functions, e.g. when evaluating an interpolated function.

Function: size_t gsl_bspline_ncoeffs (gsl_bspline_workspace * w)

This function returns the number of B-spline coefficients given by n = nbreak + k - 2.