爲什麼通過喬列斯基分解使正定矩陣反轉比使用numpy正則反轉慢？

Question

在數學上已知通過Cholesky分解來反轉正定矩陣比僅使用np.linalg.inv(X)更快。然而，當我對兩者進行實驗時，結果Cholesky分解的表現更糟！

# Inversion through Cholesky 
p = X.shape[0] 
Ip = np.eye(p) 
%timeit scipy.linalg.cho_solve(scipy.linalg.cho_factor(X,lower=True), Ip) 

The slowest run took 17.96 times longer than the fastest. This could mean that an intermediate result is being cached. 
10000 loops, best of 3: 107 µs per loop 


# Simple inversion 
%timeit np.linalg.inv(X) 

The slowest run took 58.81 times longer than the fastest. This could mean that an intermediate result is being cached. 
10000 loops, best of 3: 25.9 µs per loop 

後者縮短了。爲什麼是這樣？在R,chol2inv(chol(X))通常比solve(X)更快。

Answer 1

我對1000x1000矩陣進行了比較，通過Cholesky的反演速度大約快了一倍。