Compute Jordan normal form of matrix in Python / NumPy

问题:

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

It there an equivalent function available in NumPy and SciPy?

回答1:

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]]) 

回答2:

There's this implementation.

It will definitely not be as fast as MATLAB, though.

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