SmoothSpline: fit smoothing spline to noisy data

Fit a cubic or quintic smoothing spline to noisy data, with minimum-possible error while still having minimal roughness.

SmoothSpline is a program for obtaining the best-fit smoothing spline to a set of noisy y(x) data. This spline is "best" in the sense that it has the minimum possible error, while still having minimal roughness.

SmoothSpline calls spaps from the Matlab Curve Fitting Toolbox. While spaps(x,y,tol) returns the spline with minimal roughness for a given error tolerance, tol, the user is left to determine the appropriate tol for the best fit. SmoothSpline allows the user to either manually or automatically determine the best-fit tol.

SmoothSpline is intended for use with high-resolution, high-precision data. In this case, Epps et al. (2010) observed that there exists a critical error tolerance, above which the roughness is relatively constant (due to the "roughness" of the true underlying function) and below which the roughness increases dramatically as the spline is forced to pass closer to the noisy data.

SmoothSpline is particularly useful for determining the derivatives (dy/dx, d^2y/dx^2, …) of noisy data, which cannot be obtained accurately via finite differences.