NumCosmoMathSplineBSpline

Interpolating B-spline of order 2 to NCM_SPLINE_BSPLINE_MAX_ORDER.

Interpolates the values at the knots of NcmSpline with one control point per knot, B-spline knots placed by gsl_bspline_init_interp(), and a banded collocation solve, so preparation costs $O(n)$. Outside the knots, the value, the derivatives and the integral extrapolate the edge polynomial.

A cubic spline is $C^2$ and its interpolation error stays well above machine precision at any sample density; higher orders reach it. Maximum error at the interval midpoints for a Gaussian of mean $1200$ and standard deviation $300$ sampled uniformly on $[0, 2400]$:

On a prepared spline, ncm_spline_eval() may be called concurrently: it uses stack scratch and reads only state fixed by preparation. The derivatives and the integral use the GSL workspace and serialize on an internal lock. Preparing concurrently with any evaluation is not supported, as for every NcmSpline.