Monitor the Mahalanobis norm of the mean shift

[nikohansen]

which should be roughly between $\sqrt n$ (on a linear function) and $\sqrt{n} / \sqrt {\mu_\text{eff}}$ (under random selection, hence we probably want to normalize by $\sqrt {\mu_\text{eff}} / \sqrt{n}$). This gives an indication how much linearity the population "sees".

[nikohansen]

This would be an approximate implementation of the value, however the Mahalanobis norm should be taken before the update of the distribution parameters, because the new mean is computed with samples from the previous distribution.

def delta_mean(es):
    """return normalized delta mean"""
    n = es.mahalanobis_norm(es.mean - es.mean_old) * (
            es.sp.weights.mueff / es.N)**0.5 * es.sigma / es._sigma_old
    return n