QuadratiK: A Python and R package for clustering on the sphere and goodness-of-fit tests

We introduce QuadratiK, an open-source software, implemented in R and Python. QuadratiK supports normality tests, and two and $k$-sample tests, using kernel-based quadratic distances. The software also includes tests for uniformity on the $d$-dimensional sphere and a clustering algorithm using the Poisson kernel-based densities. Functions for generating random samples from these densities are included. These methods are encoded via object-oriented and extensively unit-tested implementations. QuadratiK offers graphical functions that enhance user experience by facilitating the validation, visualization, and interpretation of clustering results. We compare QuadratiK with related available libraries and provide illustrative code examples. In summary, QuadratiK offers a powerful suite of tools in R and Python, enabling researchers and practitioners to perform meaningful analyses and derive valid and reproducible inference across a wide range of fields. The R³ and Python⁴ codes are available under the GPL-3.0 license. Finally, we propose a dashboard application, a graphical user interface to the implemented methods, with the aim to facilitate the usage of the software among practitioners from different domains.