Python 中是否有高斯消元的标准解决方案？
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Is there a standard solution for Gauss elimination in Python?
提问by flonk
Is there somewhere in the cosmos of scipy/numpy/...a standard method for Gauss-elimination of a matrix?
scipy/numpy/...矩阵的高斯消元标准方法在宇宙中的某个地方是否存在？
One finds many snippets via google, but I would prefer to use "trusted" modules if possible.
人们通过谷歌找到了许多片段，但如果可能的话，我更愿意使用“受信任的”模块。
采纳答案by flonk
I finally found, that it can be done using LU decomposition. Here the Umatrix represents the reduced form of the linear system.
我终于发现，它可以使用LU 分解来完成。这里U矩阵表示线性系统的简化形式。
from numpy import array
from scipy.linalg import lu
a = array([[2.,4.,4.,4.],[1.,2.,3.,3.],[1.,2.,2.,2.],[1.,4.,3.,4.]])
pl, u = lu(a, permute_l=True)
Then ureads
然后u读
array([[ 2., 4., 4., 4.],
[ 0., 2., 1., 2.],
[ 0., 0., 1., 1.],
[ 0., 0., 0., 0.]])
Depending on the solvability of the system this matrix has an upper triangular or trapezoidal structure. In the above case a line of zeros arises, as the matrix has only rank 3.
根据系统的可解性，该矩阵具有上三角或梯形结构。在上述情况下，出现一行零，因为矩阵只有 rank 3。
