GNU Scientific Library Reference Manual - Third Edition (v1.12)by M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman, P. Alken, M. Booth, F. Rossi Paperback (6"x9"), 592 pages, 60 figures ISBN 0954612078 RRP £24.95 ($39.95) |

## 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 the matrix`dB`. The (i,j)-th element of`dB`is d^jB_i(x)/dx^j. The matrix`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 zeroth order derivatives in`dB`. Computing all the basis function derivatives at once is more efficient than computing 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 the matrix`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). The matrix`dB`must be of size k by at least nderiv + 1. Note that function evaluations are included as the zeroth order derivatives in`dB`. By returning only the nonzero basis functions, this function allows quantities involving linear combinations of the B_i(x) and their derivatives to be computed without unnecessary terms.

ISBN 0954612078 | GNU Scientific Library Reference Manual - Third Edition (v1.12) | See the print edition |