创建对称矩阵（numpy）
对称（实对称）矩阵也即：XT=X
step 1：创建一个方阵
>>> import numpy as np
>>> X = np.random.rand(5**2).reshape(5, 5)
>>> X
array([[ 0.26984148, 0.25408384, 0.12428487, 0.0194565 , 0.91287708],
[ 0.31837673, 0.35493156, 0.74336268, 0.31810561, 0.04409245],
[ 0.06644445, 0.8967897 , 0.10990936, 0.05036292, 0.72581982],
[ 0.94758512, 0.21375975, 0.36781736, 0.1633904 , 0.36070709],
[ 0.53263787, 0.18380491, 0.0225521 , 0.91239367, 0.75521585]])step 2：保留其上三角部分
>>> X = np.triu(X)
# 保留其上三角部分
>>> X
array([[ 0.26984148, 0.25408384, 0.12428487, 0.0194565 , 0.91287708],
[ 0. , 0.35493156, 0.74336268, 0.31810561, 0.04409245],
[ 0. , 0. , 0.10990936, 0.05036292, 0.72581982],
[ 0. , 0. , 0. , 0.1633904 , 0.36070709],
[ 0. , 0. , 0. , 0. , 0.75521585]]) step 3：将上三角”拷贝”到下三角部分
>>> X += X.T - np.diag(X.diagonal())
>>> X
array([[ 0.26984148, 0.25408384, 0.12428487, 0.0194565 , 0.91287708],
[ 0.25408384, 0.35493156, 0.74336268, 0.31810561, 0.04409245],
[ 0.12428487, 0.74336268, 0.10990936, 0.05036292, 0.72581982],
[ 0.0194565 , 0.31810561, 0.05036292, 0.1633904 , 0.36070709],
[ 0.91287708, 0.04409245, 0.72581982, 0.36070709, 0.75521585]])注意，要减去一次对角线上的元素。因为上三角cov，和下三角cov.T在进行相加时会把主对角线上的元素相加两次。
step 4：测试
>>> X.T == X
array([[ True, True, True, True, True],
[ True, True, True, True, True],
[ True, True, True, True, True],
[ True, True, True, True, True],
[ True, True, True, True, True]], dtype=bool)