<scp> maxsmooth</scp>: rapid maximally smooth function fitting with applications in Global 21-cm cosmology

Maximally Smooth Functions (MSFs) are a form of constrained functions in which there no inflection points or zero crossings high order derivatives. Consequently, they have applications to signal recovery experiments where signals interest expected be non-smooth features masked by larger smooth foregrounds. They can also act as powerful tool for diagnosing the presence systematics. The nature MSFs makes fitting these non-trivial task. We introduce maxsmooth, an open source package that uses quadratic programming rapidly fit MSFs. demonstrate efficiency and reliability maxsmooth comparison commonly used routines show we reduce time approximately two orders magnitude. implement with Partially Functions, useful describing elements structure This work has been motivated problem foreground modelling 21-cm cosmology. discuss cosmology highlight this examples using data from Experiment Detect Global Epoch Reionization Signature (EDGES) Large-aperture Dark Ages (LEDA) experiments. sinusoidal systematic EDGES log-evidence difference $86.19\pm0.12$ when compared pure fit. applied LEDA first paper identify is pip installable available download at: https://github.com/htjb/maxsmooth