Numpy中是否有内置/简易的LDU分解方法?

问题描述

我在numpy.linalg.cholesky中看到cholesky分解，但是找不到LDU分解.有人可以建议要使用的功能吗?

I see cholesky decomposition in numpy.linalg.cholesky, but could not find a LDU decompositon. Can anyone suggest a function to use?

推荐答案

Scipy具有LU分解功能: scipy.linalg.lu .请注意，这还会在混合中引入置换矩阵P. 此答案很好地解释了为什么会发生这种情况.

Scipy has an LU decomposition function: scipy.linalg.lu. Note that this also introduces a permutation matrix P into the mix. This answer gives a nice explanation of why this happens.

如果您特别需要LDU，则只需将U矩阵标准化以提取D.

If you specifically need LDU, then you can just normalize the U matrix to pull out D.

这是您可能的操作方式:

Here's how you might do it:

>>> import numpy as np
>>> import scipy.linalg as la
>>> a = np.array([[2, 4, 5],
                  [1, 3, 2],
                  [4, 2, 1]])
>>> (P, L, U) = la.lu(a)
>>> P
array([[ 0.,  1.,  0.],
       [ 0.,  0.,  1.],
       [ 1.,  0.,  0.]])
>>> L
array([[ 1.        ,  0.        ,  0.        ],
       [ 0.5       ,  1.        ,  0.        ],
       [ 0.25      ,  0.83333333,  1.        ]])
>>> U
array([[ 4. ,  2. ,  1. ],
       [ 0. ,  3. ,  4.5],
       [ 0. ,  0. , -2. ]])
>>> D = np.diag(np.diag(U))   # D is just the diagonal of U
>>> U /= np.diag(U)[:, None]  # Normalize rows of U
>>> P.dot(L.dot(D.dot(U)))    # Check
array([[ 2.,  4.,  5.],
       [ 1.,  3.,  2.],
       [ 4.,  2.,  1.]])

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