find_basis.py

import numpy as np
from matplotlib import pyplot as plt
import itertools

np.set_printoptions(precision=4, suppress=True)


def all_waves(N):
    for i in itertools.count():
        k = i + 1
        for func in [np.cos, np.sin]:
            quant = func(2 * np.pi * k/N * (np.arange(N)))
            quant = quant / np.linalg.norm(quant)
            yield quant

def all_basis(N):
    comps = list(itertools.islice(all_waves(N), N-1))
    for w1, w2 in itertools.product(comps, comps):
        yield np.reshape(w1, (N, 1)) @ np.reshape(w2, (1, N))

bases = all_basis(10)

for b1, b2 in itertools.combinations(bases, 2):
    print(b1.flatten() @ b2.flatten())