maxsmooth: Derivative Constrained Function Fitting

Harry Thomas Jones Bevins

Abstract: maxsmooth is an optimisation routine written in Python (supporting version ≥ 3.6) for fitting Derivative Constrained Functions (DCFs) to data. DCFs are a family of functions which have derivatives that do not cross zero in the band of interest. Two special cases of DCF are Maximally Smooth Functions (MSFs) which have derivatives with order m ≥ 2 constrained and Completely Smooth Functions (CSFs) with m ≥ 1 constrained. Alternatively, we can constrain an arbitrary set of derivatives and we refer to these models as Partially Smooth Functions. Due to their constrained nature, DCFs can produce perfectly smooth fits to data and reveal non-smooth signals of interest in the residuals.