python - 找出两个对称矩阵是否相同直到行/列的排列

Question

我有两个对称(项目同现)矩阵 A 和 B，想知道它们是否描述了相同的同现，只是行/列标签发生了排列。 (相同的排列必须应用于行和列以保持对称/共现属性)

例如这两个矩阵在我的测试中应该是相等的:

a = np.array([
    #1 #2 #3 #4 #5 #6 #7
    [0, 1, 1, 0, 0, 0, 1], #1
    [1, 0, 1, 2, 1, 1, 2], #2
    [1, 1, 0, 0, 0, 0, 1], #3
    [0, 2, 0, 0, 4, 0, 4], #4
    [0, 1, 0, 4, 0, 1, 2], #5
    [0, 1, 0, 0, 1, 0, 0], #6
    [1, 2, 1, 4, 2, 0, 0]  #7
])
b = np.array([
    #5 #7 #1,3#3,1#2 #4 #6
    [0, 2, 0, 0, 1, 4, 1], #5
    [2, 0, 1, 1, 2, 4, 0], #7
    [0, 1, 0, 1, 1, 0, 0], #1,3 could be either
    [0, 1, 1, 0, 1, 0, 0], #1,3 could be either
    [1, 2, 1, 1, 0, 2, 1], #2
    [4, 4, 0, 0, 2, 0, 0], #4
    [1, 0, 0, 0, 1, 0, 0]  #6
])

我目前使用 numpy.linalg.eigvals 测试特征值是否相同(我什至不确定这是一个充分条件)，但我想找到一个不相同的测试涉及数值精度，因为我在这里处理整数。

Answer 1

这是一个基于排序并利用searchsorted的矢量化解决方案-

import pandas as pd

# Sort rows for a and b
aS = np.sort(a,axis=1)
bS = np.sort(b,axis=1)

# Scale down each row to a scalar each
scale = np.r_[(np.maximum(aS.max(0),bS.max(0))+1)[::-1].cumprod()[::-1][1:],1]
aS1D = aS.dot(scale)
bS1D = bS.dot(scale)

# Use searchsorted to get the correspondence on indexing
sidx = aS1D.argsort()
searchsorted_idx = np.searchsorted(aS1D,bS1D,sorter=sidx)
searchsorted_idx[searchsorted_idx==len(aS1D)] = len(aS1D)-1
df = pd.DataFrame({'A':searchsorted_idx})
new_order = sidx[df.groupby('A').cumcount().values+searchsorted_idx]
# new_order is the permuted order, i.e. [5, 7, 1, 3, 2, 4, 6]

# Finally index into a with the new_order and compare against b
out = np.array_equal(a[new_order[:,None], new_order],b)