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Using truncted SVD for whitening gives huge speedup for me, could be done by replacing the following code:
Efac = eigen(C) ord = sortperm(Efac.values; rev=true) (v, P) = extract_kv(Efac, ord, k)
with P, v, _ = tsvd(C, k)
P, v, _ = tsvd(C, k)