在 Python/NumPy 中计算矩阵的 Jordan 标准形式 [英] Compute Jordan normal form of matrix in Python / NumPy

问题描述

在 MATLAB 中，您可以使用函数 jordan 计算矩阵的 Jordan 范式.

In MATLAB you can compute the Jordan normal form of a matrix by using the the function jordan.

NumPy 和 SciPy 中是否有等效的函数?

It there an equivalent function available in NumPy and SciPy?

推荐答案

MATLAB jordan 函数是来自 Symbolic Math Toolbox，因此从 SymPy 库中获取 Python 替代品似乎并非不合理.具体来说，Matrix 类具有方法 jordan_form.创建 sympy Matrix 时，可以将 numpy 数组作为参数传递.例如，以下内容来自维基百科关于乔丹范式的文章:

The MATLAB jordan function is from the Symbolic Math Toolbox, so it does not seem unreasonable to get its Python replacement from the SymPy library. Specifically, the Matrix class has the method jordan_form. You can pass a numpy array as an argument when you create a sympy Matrix. For example, the following is from the wikipedia article on the Jordan normal form:

In [1]: import numpy as np

In [2]: from sympy import Matrix

In [3]: a = np.array([[5, 4, 2, 1], [0, 1, -1, -1], [-1, -1, 3, 0], [1, 1, -1, 2]])

In [4]: m = Matrix(a)

In [5]: m
Out[5]: 
Matrix([
[ 5,  4,  2,  1],
[ 0,  1, -1, -1],
[-1, -1,  3,  0],
[ 1,  1, -1,  2]])

In [6]: P, J = m.jordan_form()

In [7]: J
Out[7]: 
Matrix([
[1, 0, 0, 0],
[0, 2, 0, 0],
[0, 0, 4, 1],
[0, 0, 0, 4]])

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