38.5 Evaluation of B-spline derivatives

Function: int gsl_bspline_deriv_eval (const double x, const size_t nderiv, gsl_matrix * dB, gsl_bspline_workspace * w, gsl_bspline_deriv_workspace * dw)

This function evaluates all B-spline basis function derivatives of orders 0 through nderiv (inclusive) at the position x and stores them in dB. The (i,j)th element of dB is d^j/dx^j B_i(x). dB must be of size n = nbreak + k - 2 by nderiv + 1. The value n may also be obtained by calling gsl_bspline_ncoeffs. Note that function evaluations are included as the 0th order derivatives in dB. It is far more efficient to compute all of the basis functions derivatives at once than to compute them individually, due to the nature of the defining recurrence relation.

Function: int gsl_bspline_deriv_eval_nonzero (const double x, const size_t nderiv, gsl_matrix * dB, size_t * istart, size_t * iend, gsl_bspline_workspace * w, gsl_bspline_deriv_workspace * dw)

This function evaluates all potentially nonzero B-spline basis function derivatives of orders 0 through nderiv (inclusive) at the position x and stores them in dB. The (i,j)th element of dB is d^j/dx^j B_(istart+i)(x). The last row of dB contains d^j/dx^j B_(iend)(x). dB must be of size k by at least nderiv + 1. Note that function evaluations are included as the 0th order derivatives in dB. 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.