python - 将数组从 np.triu_indices 转换为对称矩阵

Question

我可以使用以下方法轻松将对称矩阵转换为其三角形分量之一的数组/一维矩阵

A_symmetric = np.matrix([[1,2][2,3]])
A_array = A_symmetric[np.triu_indices(2)] == np.matrix([1,2,3])

(与 tril_indices 类似)

但是我如何反转这个操作，即如何从 triu_indices 给出的数组/一维矩阵中获取对称矩阵？

Answer 1

如果您可以使用数组而不是矩阵，您可以简单地进行预分配和分配:

>>> i, j = np.triu_indices(8)                                                                                       
>>> a = np.arange(i.size)                                                                                          

>>> M = np.empty((8, 8), a.dtype)
>>> M[i, j] = a                                                                                                     
>>> M[j, i] = a
>>> M                                                                                                               
array([[ 0,  1,  2,  3,  4,  5,  6,  7],                                                                            
       [ 1,  8,  9, 10, 11, 12, 13, 14],
       [ 2,  9, 15, 16, 17, 18, 19, 20],
       [ 3, 10, 16, 21, 22, 23, 24, 25],
       [ 4, 11, 17, 22, 26, 27, 28, 29],
       [ 5, 12, 18, 23, 27, 30, 31, 32],
       [ 6, 13, 19, 24, 28, 31, 33, 34],
       [ 7, 14, 20, 25, 29, 32, 34, 35]])