python - 为什么通过 Cholesky 分解反转正定矩阵比使用 numpy 进行常规反转慢？

Question

从数学上已知，通过 Cholesky 分解对正定矩阵求逆比仅使用 np.linalg.inv(X) 更快。然而，当我对两者进行试验时，发现 Cholesky 分解的性能更差!

# 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

后者耗时更短。为什么是这样？在 R 中，chol2inv(chol(X)) 通常比 solve(X) 快。

Answer 1

我对 1000x1000 矩阵进行了比较，通过 Cholesky 的反演速度大约是原来的两倍。