如何从Python中的邻接列表中选择一个子矩阵？ [英] How to select a submatrix from an adjacency list in Python?

问题描述

我有一个邻接表，其中每个数组代表该行的非零列（例如，下面的adj。列表中的第0个数组意味着第2列和第6列为1，其他所有为0）。
$ b

adj_list = [[2,6]，[1,3,24]，[2,4]，[3,5,21]，[4， 6,10]，[1,5，
7]，[6,8,9]，[7]，[7,10,14]，[5,9,11]，[10,12， 18]，[11,13]，
[12,14,15]，[9,13]，[13,16,17]，[15]，[15]，[11,19,20] ，[18]，
[18]，[4,22,23]，[21]，[21]，[2,25,26]，[24]，[24]]

b $ b

鉴于此形容词。列表中，我想选择一个具有相同的行和列索引的子矩阵，如下所示：

  submatrix =（0， 1，2，5，22）
  

子矩阵中的每个元素表示一个行号。

<1>对于子矩阵中的每一行 i ，我需要得到 iith adj_list （这相当于从一个邻接矩阵中获取 ith 行） >



2）然后从该数组中，我需要提取与子矩阵匹配的项目。例如，如果我是当前查看子矩阵中的第3个元素，它是5，那么我需要在adj_list中获得第5个数组（相当于获得第5行的adj.matrix），即[ 1,5,7]，然后我需要查看[1,5,7]中的哪些元素与子矩阵匹配（相当于获得第5行的第1，第5和第7列）。在这种情况下，第5行的结果应该是[0,1,0,1,0]，因为只有1和5在两个数组中相交）。

我可以有效地选择这个submatrix给出的形容词。

24]，[2,4]，[3,5,21]，[4,6,10]，[1,5,7]，[6,8,9]，[7]，[7,10， 14]，[13]，[16]，[17]，[15]，[14]，[15] ，[15]，[11,19,20]，[18]，[18]，[4,22,23]，[21]，[21]，[2,25,26]，[24]，[ 24]]

submatrix =（0,1,2,5,22）

结果= [[i in adj_list [sm] for i in submatrix] for sm in子矩阵]

这应该做到这一点;尽管我怀疑如果你更仔细地考虑你的最终目标，你可能更喜欢计算除此之外的其他东西。

I have an adjacency list where each array represents non-zero columns at that row (e.g. 0th array in the adj. list below means columns 2 and 6 are 1, and everything else is 0).

adj_list = [[2, 6], [1, 3, 24], [2, 4], [3, 5, 21], [4, 6, 10], [1, 5, 7], [6, 8, 9], [7], [7, 10, 14], [5, 9, 11], [10, 12, 18], [11, 13], [12, 14, 15], [9, 13], [13, 16, 17], [15], [15], [11, 19, 20], [18], [18], [4, 22, 23], [21], [21], [2, 25, 26], [24], [24]]

Given this adj. list, I would like to select a submatrix which has identical row and column indices that is given by:

submatrix = (0, 1, 2, 5, 22)

Each element in submatrix indicates a row number.

1) For each row i in submatrix, I need to get ith array from adj_list (which is equivalent to getting ith row from an adjacency matrix)

2) Then from that array, I need to extract the items that match with submatrix

For example, if I am currently looking at 3rd element in submatrix, which is 5, then I need to go to 5th array in adj_list (equivalent of getting 5th row of adj.matrix), which is [1,5,7], and then I need to look which elements in [1,5,7] matches with submatrix (equivalent of getting 1th, 5th and 7th columns of the 5th row). In this case, the result for 5th row should be [0,1,0,1,0] because only 1 and 5 are intersected in two arrays).

How can I efficiently select this submatrix given the adj. list?

解决方案

adj_list = [[2, 6], [1, 3, 24], [2, 4], [3, 5, 21], [4, 6, 10], [1, 5, 7], [6, 8, 9], [7], [7, 10, 14], [5, 9, 11], [10, 12, 18], [11, 13], [12, 14, 15], [9, 13], [13, 16, 17], [15], [15], [11, 19, 20], [18], [18], [4, 22, 23], [21], [21], [2, 25, 26], [24], [24]]

submatrix = (0, 1, 2, 5, 22)

result = [[i in adj_list[sm] for i in submatrix] for sm in submatrix]

This should do it; though I suspect you might prefer to compute something other than this if you consider your end goal more carefully.

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