The hunt for the most normal scrambler for SORM features.

most_normal.py

from scipy import linalg, stats
import numpy as np
from functools import reduce

N = 16 

def eval_scrambler(pat, reps=1):
    pat = np.atleast_1d(pat)
    D = np.diag(np.where(pat==1, -1, 1))
    H = linalg.hadamard(pat.size)
    return reduce(np.dot, [H] + [D, H] * reps)

best = -np.inf
perfs = []
for i in range(0, 1<<N):
    pat = np.asarray([(i >> b) & 1 for b in range(N)])
    T = eval_scrambler(pat, reps=2)
    vals = np.unique(T)
    (_, perf) = stats.shapiro(T.flatten())
    perfs.append(perf)

    if perf > best:
        best = perf
        print('%s -> %s' % (pat, perf))

print(stats.itemfreq(perfs))