Input normalization fails when ensemble size in EKI less than number of parameters

[eviatarbach]

When normalizing inputs from input–output pairs that come from EKI, if m (ensemble size) is less than p (number of parameters), then cov(get_inputs(input_output_pairs), dims = 2) in Emulators.jl is rank-deficient, which causes problems when it is inverted in order to normalize the inputs. Note that even if there are multiple EKI iterations, assuming no localization or additive inflation is applied, then each iteration will still be in the same subspace as the initial ensemble.

As an alternative, the normalization could be performed in the ensemble subspace.