在python中获取方矩阵的上三角或下三角的所有元素 [英] Get all elements of the upper or lower triangle of a square matrix in python

问题描述

在numpy/scipy中是否有一个函数可以返回方矩阵的三角形之一(上或下)的所有元素?

Is there a function in numpy/scipy that returns all the elements of one of the triangles (upper or lower) of a square matrix?

例如:

matrix = [[1,  2,  3],
          [4,  5,  6],
          [7,  8,  9]]

三角形(上下):

up = [1,2,3,5,6,9]
down = [1,4,5,7,8,9]

或

up = [1,2,5,3,6,9]
down = [1,4,7,5,8,9]

谢谢！

是的，有两个功能可以帮助您做到这一点:np.triu_indices(n)(用于上部三角形)和np.tril_indices(n)(用于下部三角形).

Yes there are two functions that help you do that: np.triu_indices(n) (for the upper triangle) and np.tril_indices(n) (for the lower triangle).

感谢katrielalex！

Thanks katrielalex!

推荐答案

元素的顺序重要吗?

通常，矩阵的上下三角形围绕 other 对角线(从左上方到右下方)获取.要解决此问题，您需要在两个对角线之间翻转"，这可以使用np.fliplr(matrix)进行.这将为您提供正确的元素，但顺序为自然"(逐行，每行越来越短).您还可以通过翻转另一种方式(np.flipud)获得逐列顺序.但是我不知道有什么方法可以获取正在使用的按较小的对角线读数"的顺序，而不能一次读取一个对角线的矩阵.

Normally the upper and lower triangles of a matrix are taken about the other diagonal (top left to bottom right). To fix that, you need to "flip" between the two diagonals, which you can do with np.fliplr(matrix). That will get you the correct elements, but in the "natural" order (row-by-row, with each row getting shorter). You can also get the column-by-column order by flipping the other way (np.flipud). But I don't know any way to get the "reading by smaller diagonals" order that you are using, short of reading the matrix one diagonal at a time.

要获取对角线元素，可以使用np.triu_indices(对于下部三角形为np.tril_indices)获取它们的索引，然后通过它们进行索引.

To get the diagonal elements you can get their indices with np.triu_indices (or, for the lower triangle, np.tril_indices) and then index by them.

>>> matrix
array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])
>>> np.fliplr(matrix)[np.triu_indices(3)]
array([3, 2, 1, 5, 4, 7])

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