消除不符合匹配条件的数组行 [英] Eliminating array rows that do not meet a matching criterion

问题描述

考虑由成对的元素组成的数组M.(我用空格来强调我们将要处理元素对).实际的数组将具有大量的行和4,6,8或10列.

Consider an array, M, made up of pairs of elements. (I've used spaces to emphasize that we will be dealing with element PAIRS). The actual arrays will have a large number of rows, and 4,6,8 or 10 columns.

import numpy as np

M = np.array([[1,3,  2,1,  4,2,  3,3],
              [3,5,  6,9,  5,1,  3,4],
              [1,3,  2,4,  3,4,  7,2],
              [4,5,  1,2,  2,1,  2,3],
              [6,4,  4,1,  6,1,  4,7],
              [6,7,  7,6,  9,7,  6,2],
              [5,3,  1,5,  3,3,  3,3]])

问题::我想从M中删除具有该元素对与该行中任何其他对没有共同元素的行.

PROBLEM: I want to eliminate rows from M having an element pair that has no common elements with any of the other pairs in that row.

在数组M中，应删除第二行和第四行.原因如下:
第二行:该对(6,9)与(3,5)，(5,1)或(3,4)没有共同的元素
第4行:对(4,5)与(1,2)，(2,1)或(2,3)没有共同的元素

In array M, the 2nd row and the 4th row should be eliminated. Here's why:
2nd row: the pair (6,9) has no common element with (3,5), (5,1), or (3,4)
4th row: the pair (4,5) has no common element with (1,2), (2,1), or (2,3)

我确定有一个不错的广播解决方案，但我看不到.

I'm sure there's a nice broadcasting solution, but I can't see it.

推荐答案

这是一种广播解决方案.希望这是不言自明的:

This is a broadcasting solution. Hope it's self-explained:

a = M.reshape(M.shape[0],-1,2)

mask = ~np.eye(a.shape[1], dtype=bool)[...,None]

is_valid = (((a[...,None,:]==a[:,None,...])&mask).any(axis=(-1,-2))
            |((a[...,None,:]==a[:,None,:,::-1])&mask).any(axis=(-1,-2))
           ).all(-1)

M[is_valid]

输出:

array([[1, 3, 2, 1, 4, 2, 3, 3],
       [1, 3, 2, 4, 3, 4, 7, 2],
       [6, 4, 4, 1, 6, 1, 4, 7],
       [6, 7, 7, 6, 9, 7, 6, 2],
       [5, 3, 1, 5, 3, 3, 3, 3]])

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