Numerical Recipes-inspired interpolating cubic splines - #89
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June 23, 2026 17:43
…Just contains the CC0 code, plus a routine for between-knot derivatives.
derivatives are shown, integrals were left out.
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This code has proven invaluable to my work with Stan. Kharratzadeh's B-spline routines, while nice, didn't offer integrals. I also needed a way to control the slope at one end, and guarantee it passed through a specific point. As luck would have it, I had reconstructed Numerical Recipes' interpolating cubic spline code a few years earlier, which made it easy to analytically work out those integrals. It also had a built-in method for controlling the initial and terminal slope of the spline. I've added code to calculate the derivative (the second derivative is just linear interpolation, so there's no point).
In a deterministic context, this code can be quite a bit faster than Kharratzadeh's B-splines, as it has runtime$O(n)$ versus Kharratzadeh's $O(n^2)$ . Unfortunately, it can behave poorly in the sampling loop, to the point that Kharratzadeh's may still wind up faster for very large $n$ .
The license on this code is CC0, as a lot of it is just the raw math but tidied up to be a bit faster.