Root-covariance types

Consensus-Based Sampling uses the usual matrix square root to compute the root-covariance matrix $V_\alpha^{\frac{1}{2}}(x_t)$ (option root = :SymmetricRoot). However, an alternative, non-symmetric, distributionally equivalent approach is given in A. Garbuno-Inigo, N. Nüsken, and S. Reich (2020) (option root = :AsymmetricRoot).

By default, CBS uses root = :AsymmetricRoot if N <= 10 * D, and root = :SymmetricRoot otherwise, as this approach gives (roughly) the best performance.