有人能解释为什么逆不与这个矩阵工作，但它是与注释部分?
from sympy import Matrix
list = []
print(self.get_key_secret())
key = np.array([7, 23, 21, 9, 19, 3, 15, 15, 12]).reshape(3, 3)
# key = np.array(
# [[3, 10, 20],
# [20, 9, 17],
# [9, 4, 17]])
print(self.get_message_secret().shape)
encr = np.matmul(self.get_message_secret(), key)
encr = encr % 26
inverse_keyArray = Matrix(key).inv_mod(26)
print(inverse_keyArray)
inverse_keyArray = np.array(inverse_keyArray).astype(float)
print(inverse_keyArray)
decryption = np.matmul(encr, inverse_keyArray)
res = np.remainder(decryption, 26)
print(res)
我得到错误
ValueError: inverse of -3318 (mod 26) does not exist
sympy.matrices.common.NonInvertibleMatrixError: Matrix is not invertible (mod 26)
我本来想抱怨缺少self.get_key_secret()之类的项目，但意识到inv只涉及key数组:
In [1]: key = np.array([7, 23, 21, 9, 19, 3, 15, 15, 12]).reshape(3, 3)
In [2]: key
Out[2]:
array([[ 7, 23, 21],
[ 9, 19, 3],
[15, 15, 12]])
我从那得到一个sympy.Matrix:
In [3]: Matrix(key)
Out[3]:
⎡7 23 21⎤
⎢ ⎥
⎢9 19 3 ⎥
⎢ ⎥
⎣15 15 12⎦
完整的错误，带回溯。诚然，它并没有增加多少。部分原因是我不熟悉这个mod逆。
In [4]: Matrix(key).inv_mod(26)
-----------------------------------------------------------------------
ValueError Traceback (most recent call last)
File /usr/local/lib/python3.8/dist-packages/sympy/matrices/inverse.py:176, in _inv_mod(M, m)
175 try:
--> 176 det_inv = mod_inverse(det_K, m)
177 except ValueError:
File /usr/local/lib/python3.8/dist-packages/sympy/core/numbers.py:551, in mod_inverse(a, m)
550 if c is None:
--> 551 raise ValueError('inverse of %s (mod %s) does not exist' % (a, m))
552 return c
ValueError: inverse of -3318 (mod 26) does not exist
During handling of the above exception, another exception occurred:
NonInvertibleMatrixError Traceback (most recent call last)
Input In [4], in <cell line: 1>()
----> 1 Matrix(key).inv_mod(26)
File /usr/local/lib/python3.8/dist-packages/sympy/matrices/matrices.py:2199, in MatrixBase.inv_mod(self, m)
2198 def inv_mod(self, m):
-> 2199 return _inv_mod(self, m)
File /usr/local/lib/python3.8/dist-packages/sympy/matrices/inverse.py:178, in _inv_mod(M, m)
176 det_inv = mod_inverse(det_K, m)
177 except ValueError:
--> 178 raise NonInvertibleMatrixError('Matrix is not invertible (mod %d)' % m)
180 K_adj = M.adjugate()
181 K_inv = M.__class__(N, N,
182 [det_inv * K_adj[i, j] % m for i in range(N) for j in range(N)])
NonInvertibleMatrixError: Matrix is not invertible (mod 26)
所以这个错误与numpy和sympy的混合无关，因为它使用的是sympy矩阵。
常见的数值矩阵逆工作:
In [6]: np.linalg.inv(key)
Out[6]:
array([[-0.05515371, -0.01175407, 0.0994575 ],
[ 0.01898734, 0.06962025, -0.05063291],
[ 0.04520796, -0.07233273, 0.02230259]])
和等效分数版本
In [9]: Matrix(key).inv()
Out[9]:
⎡-61 -13 55 ⎤
⎢──── ──── ─── ⎥
⎢1106 1106 553 ⎥
⎢ ⎥
⎢ 11 ⎥
⎢3/158 ─── -4/79⎥
⎢ 158 ⎥
⎢ ⎥
⎢ 25 -40 37 ⎥
⎢ ─── ──── ──── ⎥
⎣ 553 553 1659 ⎦
尝试其他mod:
In [15]: Matrix(key).inv_mod(5)
Out[15]:
⎡4 2 0⎤
⎢ ⎥
⎢1 2 4⎥
⎢ ⎥
⎣0 0 3⎦
也适用于5的其他幂
我认为你不需要将sympy矩阵对象转换为numpy，因为sympy处理矩阵乘法(使用相同的@运算符)，并且你只使用2d矩阵-你不需要numpymatmul的"批处理"功能。
例如:
In [32]: M = Matrix(key)
In [33]: M1= M.inv_mod(5)
In [34]: M@M1
Out[34]:
⎡51 60 155⎤
⎢ ⎥
⎢55 56 85 ⎥
⎢ ⎥
⎣75 60 96 ⎦
使用sympy可以避免浮点数逆运算的问题。
In [38]: M@M.inv()
Out[38]:
⎡1 0 0⎤
⎢ ⎥
⎢0 1 0⎥
⎢ ⎥
⎣0 0 1⎦
In [39]: key@np.linalg.inv(key)
Out[39]:
array([[1.00000000e+00, 2.22044605e-16, 0.00000000e+00],
[0.00000000e+00, 1.00000000e+00, 1.24900090e-16],
[1.11022302e-16, 0.00000000e+00, 1.00000000e+00]])