Question

数学上已知通过Cholesky分解反转正定矩阵比仅使用# 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更快。然而，当我对两者进行实验时，事实证明Cholesky分解的表现更差！

后者缩短了。为什么是这样？在chol2inv(chol(X))中，solve(X)通常比<table id="companies" class="table table-striped table-bordered table-hover"> <thead> <tr> <th class="center"> Id </th> <th>RegNo</th> <th>Name</th> <th class="hidden-480">Industry</th> <th class="hidden-phone"> Size </th> <th class="hidden-480">LineOfDefence</th> <th>Address</th> </tr> </thead> </table>更快。

Answer 1

我在1000x1000矩阵上进行比较，而通过Cholesky的反转速度大约是其两倍。

Answer 2

也许您的矩阵太小。我只是在Matlab中使用Cholesky分解然后进行LU分解测试了矩阵反转，得到了一个2×2的矩阵。使用Cholesky进行999999次重复需要5秒，而使用LU仅需3.4秒。确实，Cholesky算法及其后向替换算法具有较小的大O结果，但该结果是渐近结果，仅适用于大矩阵。

#LU decomposition
tic
for i=1:999999
    (V_i(:,:,2)+[0 1e-10;0 0])\eye(2);
end
toc
Elapsed time is 3.430676 seconds.

#Cholesky
tic
for i=1:999999
    (V_i(:,:,2))\eye(2);
end
toc
Elapsed time is 4.824175 seconds.

Answer 3

np.linalg.inv使用并行处理。运行两个功能时，请检查您的CPU峰值。如果您使用并行处理来运行多个inv或Cholesky，则会发现Cholesky更快。

为什么通过Cholesky分解反转正定矩阵比使用numpy的常规反转慢？

3 个答案: