从NumPy数组中选择特定的行和列

I've been going crazy trying to figure out what stupid thing I'm doing wrong here.

我一直想弄明白我做错了什么蠢事。

I'm using NumPy, and I have specific row indices and specific column indices that I want to select from. Here's the gist of my problem:

我使用NumPy，我有特定的行索引和特定的列索引，我想从中选择。下面是我的问题的要点:

import numpy as np

a = np.arange(20).reshape((5,4))
# array([[ 0,  1,  2,  3],
#        [ 4,  5,  6,  7],
#        [ 8,  9, 10, 11],
#        [12, 13, 14, 15],
#        [16, 17, 18, 19]])

# If I select certain rows, it works
print a[[0, 1, 3], :]
# array([[ 0,  1,  2,  3],
#        [ 4,  5,  6,  7],
#        [12, 13, 14, 15]])

# If I select certain rows and a single column, it works
print a[[0, 1, 3], 2]
# array([ 2,  6, 14])

# But if I select certain rows AND certain columns, it fails
print a[[0,1,3], [0,2]]
# Traceback (most recent call last):
#   File "<stdin>", line 1, in <module>
# ValueError: shape mismatch: objects cannot be broadcast to a single shape

Why is this happening? Surely I should be able to select the 1st, 2nd, and 4th rows, and 1st and 3rd columns? The result I'm expecting is:

为什么会这样?当然，我应该能够选择1、2、4行、1、3列?我期待的结果是:

a[[0,1,3], [0,2]] => [[0,  2],
                      [4,  6],
                      [12, 14]]

3 个解决方案

#1

Fancy indexing requires you to provide all indices for each dimension. You are providing 3 indices for the first one, and only 2 for the second one, hence the error. You want to do something like this:

花哨的索引要求您提供每个维度的所有索引。您为第一个提供了3个索引，为第二个提供了2个索引，因此出现了错误。你想做这样的事情:

>>> a[[[0, 0], [1, 1], [3, 3]], [[0,2], [0,2], [0, 2]]]
array([[ 0,  2],
       [ 4,  6],
       [12, 14]])

That is of course a pain to write, so you can let broadcasting help you:

写这篇文章当然很痛苦，所以你可以让广播帮助你:

>>> a[[[0], [1], [3]], [0, 2]]
array([[ 0,  2],
       [ 4,  6],
       [12, 14]])

This is much simpler to do if you index with arrays, not lists:

如果你用数组而不是列表来索引，这就简单多了:

>>> row_idx = np.array([0, 1, 3])
>>> col_idx = np.array([0, 2])
>>> a[row_idx[:, None], col_idx]
array([[ 0,  2],
       [ 4,  6],
       [12, 14]])

#2

As Toan suggests, a simple hack would be to just select the rows first, and then select the columns over that.

正如Toan所建议的，一个简单的技巧是先选择行，然后再选择上面的列。

>>> a[[0,1,3], :]            # Returns the rows you want
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [12, 13, 14, 15]])
>>> a[[0,1,3], :][:, [0,2]]  # Selects the columns you want as well
array([[ 0,  2],
       [ 4,  6],
       [12, 14]])

[Edit] The built-in method: np.ix_

I recently discovered that numpy gives you an in-built one-liner to doing exactly what @Jaime suggested, but without having to use broadcasting syntax (which suffers from lack of readability). From the docs:

我最近发现numpy提供了一个内置的一行程序来执行@Jaime建议的操作，但是不需要使用广播语法(因为缺乏可读性)。从文档:

Using ix_ one can quickly construct index arrays that will index the cross product. a[np.ix_([1,3],[2,5])] returns the array [[a[1,2] a[1,5]], [a[3,2] a[3,5]]].

使用ix_one可以快速构建索引数组，从而索引跨产品。[np.ix_([1,3],[2、5]))返回的数组([[1,2][1,5]],[[3 2]一个[3,5]]]。

So you use it like this:

你可以这样使用它:

>>> a = np.arange(20).reshape((5,4))
>>> a[np.ix_([0,1,3], [0,2])]
array([[ 0,  2],
       [ 4,  6],
       [12, 14]])

And the way it works is that it takes care of aligning arrays the way Jaime suggested, so that broadcasting happens properly:

它的工作方式是按照Jaime建议的方式对数组进行对齐，这样广播才能正常进行:

>>> np.ix_([0,1,3], [0,2])
(array([[0],
        [1],
        [3]]), array([[0, 2]]))

Also, as MikeC says in a comment, np.ix_ has the advantage of returning a view, which my first (pre-edit) answer did not. This means you can now assign to the indexed array:

另外，正如MikeC在评论中所说，np。ix_具有返回视图的优势，而我的第一个(预编辑)答案则没有。这意味着您现在可以分配给索引数组:

>>> a[np.ix_([0,1,3], [0,2])] = -1
>>> a    
array([[-1,  1, -1,  3],
       [-1,  5, -1,  7],
       [ 8,  9, 10, 11],
       [-1, 13, -1, 15],
       [16, 17, 18, 19]])

#3

USE:

使用:

 >>> a[[0,1,3]][:,[0,2]]
array([[ 0,  2],
   [ 4,  6],
   [12, 14]])

OR:

或者:

>>> a[[0,1,3],::2]
array([[ 0,  2],
   [ 4,  6],
   [12, 14]])