我的理解是，numpy.correlate和numpy.corrcoef对于对齐的归一化向量应该产生相同的结果。两个直接的情况正好相反：

from math import isclose as near
import numpy as np

def normalizedCrossCorrelation(a, b):
    assert len(a) == len(b)
    normalized_a = [aa / np.linalg.norm(a) for aa in a]
    normalized_b = [bb / np.linalg.norm(b) for bb in b]
    return np.correlate(normalized_a, normalized_b)[0]

def test_normalizedCrossCorrelationOfSimilarVectorsRegression0():
    v0 = [1, 2, 3, 2, 1, 0, -2, -1, 0]
    v1 = [1, 1.9, 2.8, 2, 1.1, 0, -2.2, -0.9, 0.2]
    assert near(normalizedCrossCorrelation(v0, v1), 0.9969260391224474)
    print(f"{np.corrcoef(v0, v1)=}")
    assert near(normalizedCrossCorrelation(v0, v1), np.corrcoef(v0, v1)[0, 1])

def test_normalizedCrossCorrelationOfSimilarVectorsRegression1():
    v0 = [1, 2, 3, 2, 1, 0, -2, -1, 0]
    v1 = [0.8, 1.9, 2.5, 2.1, 1.2, -0.3, -2.4, -1.4, 0.4]
    assert near(normalizedCrossCorrelation(v0, v1), 0.9809817769512982)
    print(f"{np.corrcoef(v0, v1)=}")
    assert near(normalizedCrossCorrelation(v0, v1), np.corrcoef(v0, v1)[0, 1])

Pytest输出：

E       assert False
E        +  where False = near(0.9969260391224474, 0.9963146417122921)
E        +    where 0.9969260391224474 = normalizedCrossCorrelation([1, 2, 3, 2, 1, 0, ...], [1, 1.9, 2.8, 2, 1.1, 0, ...])

E       assert False
E        +  where False = near(0.9809817769512982, 0.9826738919606931)
E        +    where 0.9809817769512982 = normalizedCrossCorrelation([1, 2, 3, 2, 1, 0, ...], [0.8, 1.9, 2.5, 2.1, 1.2, -0.3, ...])