我可以将自己的Python类与numpy或其他矩阵库一起使用吗? [英] Can I use my own Python class with numpy or some other matrix library?

问题描述

我希望能够使用Python类作为元素来进行矩阵运算-在这种情况下，一个简单的

I'd like to be able to do matrix operations using a Python class as the elements—in this case, a simple Galois field implementation. It implements the necessary __add__, __mul__, __sub__ etc.

起初，我认为可以使用 numpy数组，使用dtype参数，但来自 dtype文档，看来dtype不能是任意的Python类.例如，我有一个类Galois可以对模2进行运算:

At first, I thought this should be possible with numpy arrays, using the dtype parameter, but from the dtype documentation, it seems that dtype can't be an arbitrary Python class. For example, I have a class Galois which does operations modulo 2:

>>> from galois import Galois
>>> Galois(1) + Galois(0)
Galois(1)
>>> Galois(1) + Galois(1)
Galois(0)

我可以尝试在numpy中使用它:

I can try to use this in numpy:

>>> import numpy as np
>>> a = np.identity(4, Galois)
>>> a
array([[1, 0, 0, 0],
       [0, 1, 0, 0],
       [0, 0, 1, 0],
       [0, 0, 0, 1]], dtype=object)

但是，如果我对矩阵进行运算，则元素将不遵循类的方法:

But if I do operations on the matrices, the elements aren't following the methods of my class:

>>> b = np.identity(4, Galois)
>>> a+b
array([[2, 0, 0, 0],
       [0, 2, 0, 0],
       [0, 0, 2, 0],
       [0, 0, 0, 2]], dtype=object)

有什么办法可以使numpy正常工作吗?

Is there any way to make this work with numpy?

是否还有其他Python矩阵库可以对任意数字类进行矩阵运算(包括求逆)?

Is there any other Python matrix library that can do matrix operations (including inversion) on an arbitrary number-like class?

感谢您到目前为止的回答.但是我仍然无法如我所愿地真正使用它.加法和乘法看起来不错，但矩阵求逆却不好.例如，让我们尝试获取 AES逆S盒仿射变换矩阵从转发S-box仿射变换矩阵.

Thanks for the answers so far. But I'm still not able to really use it as I hoped. Adds and multiplies seem good, but not matrix inversion. For example, let's try to get the AES inverse S-box affine transform matrix from the forward S-box affine transform matrix.

class Galois(object):
    MODULO = 2

    def __init__(self, val):
        self.val = int(val) % self.MODULO

    def __add__(self, val):
        return self.__class__((self.val + int(val)) % self.MODULO)
    def __sub__(self, val):
        return self.__class__((self.val - int(val)) % self.MODULO)
    def __mul__(self, val):
        return self.__class__((self.val * int(val)) % self.MODULO)
    def __int__(self):
        return self.val
    def __repr__(self):
        return "%s(%d)" % (self.__class__.__name__, self.val)
    def __float__(self):
        return float(self.val)

if __name__ == "__main__":
    import numpy as np

    Gv = np.vectorize(Galois)

    a = Gv(np.identity(8)) + Gv(np.eye(8,8,-1)) + Gv(np.eye(8,8,-2)) + Gv(np.eye(8,8,-3)) + Gv(np.eye(8,8,-4)) + Gv(np.eye(8,8,4)) + Gv(np.eye(8,8,5)) + Gv(np.eye(8,8,6)) + Gv(np.eye(8,8,7))
    print np.matrix(a)
    print np.matrix(a).I

结果:

[[Galois(1) Galois(0) Galois(0) Galois(0) Galois(1) Galois(1) Galois(1)
  Galois(1)]
 [Galois(1) Galois(1) Galois(0) Galois(0) Galois(0) Galois(1) Galois(1)
  Galois(1)]
 [Galois(1) Galois(1) Galois(1) Galois(0) Galois(0) Galois(0) Galois(1)
  Galois(1)]
 [Galois(1) Galois(1) Galois(1) Galois(1) Galois(0) Galois(0) Galois(0)
  Galois(1)]
 [Galois(1) Galois(1) Galois(1) Galois(1) Galois(1) Galois(0) Galois(0)
  Galois(0)]
 [Galois(0) Galois(1) Galois(1) Galois(1) Galois(1) Galois(1) Galois(0)
  Galois(0)]
 [Galois(0) Galois(0) Galois(1) Galois(1) Galois(1) Galois(1) Galois(1)
  Galois(0)]
 [Galois(0) Galois(0) Galois(0) Galois(1) Galois(1) Galois(1) Galois(1)
  Galois(1)]]
[[ 0.4  0.4 -0.6  0.4  0.4 -0.6  0.4 -0.6]
 [-0.6  0.4  0.4 -0.6  0.4  0.4 -0.6  0.4]
 [ 0.4 -0.6  0.4  0.4 -0.6  0.4  0.4 -0.6]
 [-0.6  0.4 -0.6  0.4  0.4 -0.6  0.4  0.4]
 [ 0.4 -0.6  0.4 -0.6  0.4  0.4 -0.6  0.4]
 [ 0.4  0.4 -0.6  0.4 -0.6  0.4  0.4 -0.6]
 [-0.6  0.4  0.4 -0.6  0.4 -0.6  0.4  0.4]
 [ 0.4 -0.6  0.4  0.4 -0.6  0.4 -0.6  0.4]]

不是我希望的结果.似乎对于矩阵求逆，numpy只是将矩阵转换为浮点数，然后使用纯实数进行求逆.

Not the result I hoped for. It seems that for the matrix inversion, numpy just converts the matrix to floats, then does the inversion with plain real numbers.

推荐答案

您可以将object用作dtype，这将允许任意Python对象.我认为没有什么办法可以专门化一个numpy数组，使其仅接受一个特定类的Python对象.

You can use object as the dtype, which will allow arbitrary Python objects. I don't think there's any way of specializing a numpy array to accept only one particular class of Python object.

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