CaTchDes: MATLAB codes for Caratheodory–Tchakaloff Near-Optimal Regression Designs

We provide a MATLAB package for the computation of near-optimal sampling sets and weights (designs) for $n$-th degree polynomial regression on discretizations of planar, surface and solid domains. This topic has strong connections with computational statistics and approximation theory. Optimality has two aspects that are here treated together: the cardinality of the sampling set, and the quality of the regressor (its prediction variance in statistical terms, its uniform operator norm in approximation theoretic terms). The regressor quality is measured by a threshold (design G-optimality) and reached by a standard multiplicative algorithm. Low sampling cardinality is then obtained via Caratheodory-Tchakaloff discrete measure concentration. All the steps are carried out using native MATLAB functions, such as the qr factorization and the lsqnonneg quadratic minimizer.