Python 为什么 numpy 矩阵乘法计算时间在 100x100 时增加一个数量级

When computing A @ a where A is a random N by N matrix and a is a vector with N random elements using numpy the computation time jumps by an order of magnitude at N=100. Is there any particular reason for this? As a comparison the same operation using torch on the cpu has a more gradual increase

用同样的行为try 了python3.10、3.9和3.7

用于生成图形的Numpy部分的代码:

import numpy as np
from tqdm.notebook import tqdm
import pandas as pd
import time
import sys

def sym(A):
    return .5 * (A + A.T)

results = []
for n in tqdm(range(2, 500)):
    for trial_idx in range(10):
        A = sym(np.random.randn(n, n))
        a = np.random.randn(n)        
        
        t = time.time()
        for i in range(1000):
            A @ a
        t = time.time() - t
        results.append({
            'n': n,
            'time': t,
            'method': 'numpy',
        })
results = pd.DataFrame(results)

from matplotlib import pyplot as plt
fig, ax = plt.subplots(1, 1)
ax.semilogy(results.n.unique(), results.groupby('n').time.mean(), label="numpy")
ax.set_title(f'A @ a timimgs (1000 times)\nPython {sys.version.split(" ")[0]}')
ax.legend()
ax.set_xlabel('n')
ax.set_ylabel('avg. time')

更新

添加

import os
os.environ["MKL_NUM_THREADS"] = "1" 
os.environ["NUMEXPR_NUM_THREADS"] = "1" 
os.environ["OMP_NUM_THREADS"] = "1" 

before ìmport numpy gives a more expected output, see this answer for details: https://stackoverflow.com/a/74662135/5043576