用2个索引列表索引2D Numpy数组 [英] Index a 2D Numpy array with 2 lists of indices
问题描述
我有一个奇怪的情况.
I've got a strange situation.
我有一个二维的Numpy数组，x:
I have a 2D Numpy array, x:
x = np.random.random_integers(0,5,(20,8))
我有2个索引器-一个索引为行，一个索引为列.为了索引X，我必须执行以下操作:
And I have 2 indexers--one with indices for the rows, and one with indices for the column. In order to index X, I am having to do the following:
row_indices = [4,2,18,16,7,19,4]
col_indices = [1,2]
x_rows = x[row_indices,:]
x_indexed = x_rows[:,column_indices]
不仅仅是:
x_new = x[row_indices,column_indices]
(失败:错误，无法通过(2，)广播(20，))
(which fails with: error, cannot broadcast (20,) with (2,))
我希望能够使用广播在一行中建立索引，因为这样可以使代码保持干净和可读性...而且，我对幕后的python并不太了解，但是据我所知，它在一行中应该更快(并且我将使用相当大的数组).
I'd like to be able to do the indexing in one line using the broadcasting, since that would keep the code clean and readable...also, I don't know all that much about python under the hood, but as I understand it, it should be faster to do it in one line (and I'll be working with pretty big arrays).
测试用例:
x = np.random.random_integers(0,5,(20,8))
row_indices = [4,2,18,16,7,19,4]
col_indices = [1,2]
x_rows = x[row_indices,:]
x_indexed = x_rows[:,col_indices]
x_doesnt_work = x[row_indices,col_indices]
推荐答案
使用np.ix_使用索引或布尔数组/掩码进行选择或分配
1.使用indexing-arrays
A.选择
Selections or assignments with np.ix_ using indexing or boolean arrays/masks
1. With indexing-arrays
A. Selection
我们可以使用 np.ix_ 来获取索引数组的元组，它们可彼此广播以导致索引的高维组合.因此，当该元组用于索引输入数组时，将为我们提供相同的高维数组.因此，要基于两个1D索引数组进行选择，它将是-
We can use np.ix_ to get a tuple of indexing arrays that are broadcastable against each other to result in a higher-dimensional combinations of indices. So, when that tuple is used for indexing into the input array, would give us the same higher-dimensional array. Hence, to make a selection based on two 1D indexing arrays, it would be -
x_indexed = x[np.ix_(row_indices,col_indices)]
B.分配
我们可以使用相同的符号将标量或可广播数组分配给那些索引位置.因此，以下用于分配的作品-
We can use the same notation for assigning scalar or a broadcastable array into those indexed positions. Hence, the following works for assignments -
x[np.ix_(row_indices,col_indices)] = # scalar or broadcastable array
2.使用masks
我们也可以将布尔数组/掩码与np.ix_一起使用，类似于使用索引数组的方式.可以再次使用它来选择输入数组中的一个块，也可以对其进行分配.
2. With masks
We can also use boolean arrays/masks with np.ix_, similar to how indexing arrays are used. This can be used again to select a block off the input array and also for assignments into it.
A.选择
因此，分别使用row_mask和col_mask布尔数组作为行和列选择的掩码，我们可以使用以下内容进行选择-
Thus, with row_mask and col_mask boolean arrays as the masks for row and column selections respectively, we can use the following for selections -
x[np.ix_(row_mask,col_mask)]
B.分配
以下内容适用于作业-
x[np.ix_(row_mask,col_mask)] = # scalar or broadcastable array
样品运行
1.将np.ix_与indexing-arrays
Sample Runs
1. Using np.ix_ with indexing-arrays
输入数组和索引数组-
In [221]: x
Out[221]:
array([[17, 39, 88, 14, 73, 58, 17, 78],
[88, 92, 46, 67, 44, 81, 17, 67],
[31, 70, 47, 90, 52, 15, 24, 22],
[19, 59, 98, 19, 52, 95, 88, 65],
[85, 76, 56, 72, 43, 79, 53, 37],
[74, 46, 95, 27, 81, 97, 93, 69],
[49, 46, 12, 83, 15, 63, 20, 79]])
In [222]: row_indices
Out[222]: [4, 2, 5, 4, 1]
In [223]: col_indices
Out[223]: [1, 2]
具有np.ix_-
In [224]: np.ix_(row_indices,col_indices) # Broadcasting of indices
Out[224]:
(array([[4],
[2],
[5],
[4],
[1]]), array([[1, 2]]))
做出选择-
In [225]: x[np.ix_(row_indices,col_indices)]
Out[225]:
array([[76, 56],
[70, 47],
[46, 95],
[76, 56],
[92, 46]])
由OP建议 ，实际上与使用row_indices的2D数组版本的 old-school 广播相同，该版本的元素/索引被发送到axis=0，从而创建axis=1处的单个尺寸，因此允许使用col_indices进行广播.因此，我们将有一个类似的替代解决方案-
As suggested by OP, this is in effect same as performing old-school broadcasting with a 2D array version of row_indices that has its elements/indices sent to axis=0 and thus creating a singleton dimension at axis=1 and thus allowing broadcasting with col_indices. Thus, we would have an alternative solution like so -
In [227]: x[np.asarray(row_indices)[:,None],col_indices]
Out[227]:
array([[76, 56],
[70, 47],
[46, 95],
[76, 56],
[92, 46]])
如前所述，对于作业，我们只是这样做.
As discussed earlier, for the assignments, we simply do so.
行，列索引数组-
In [36]: row_indices = [1, 4]
In [37]: col_indices = [1, 3]
使用标量进行分配-
In [38]: x[np.ix_(row_indices,col_indices)] = -1
In [39]: x
Out[39]:
array([[17, 39, 88, 14, 73, 58, 17, 78],
[88, -1, 46, -1, 44, 81, 17, 67],
[31, 70, 47, 90, 52, 15, 24, 22],
[19, 59, 98, 19, 52, 95, 88, 65],
[85, -1, 56, -1, 43, 79, 53, 37],
[74, 46, 95, 27, 81, 97, 93, 69],
[49, 46, 12, 83, 15, 63, 20, 79]])
使用2D块(可广播数组)进行分配-
Make assignments with 2D block(broadcastable array) -
In [40]: rand_arr = -np.arange(4).reshape(2,2)
In [41]: x[np.ix_(row_indices,col_indices)] = rand_arr
In [42]: x
Out[42]:
array([[17, 39, 88, 14, 73, 58, 17, 78],
[88, 0, 46, -1, 44, 81, 17, 67],
[31, 70, 47, 90, 52, 15, 24, 22],
[19, 59, 98, 19, 52, 95, 88, 65],
[85, -2, 56, -3, 43, 79, 53, 37],
[74, 46, 95, 27, 81, 97, 93, 69],
[49, 46, 12, 83, 15, 63, 20, 79]])
2.将np.ix_与masks
2. Using np.ix_ with masks
输入数组-
In [19]: x
Out[19]:
array([[17, 39, 88, 14, 73, 58, 17, 78],
[88, 92, 46, 67, 44, 81, 17, 67],
[31, 70, 47, 90, 52, 15, 24, 22],
[19, 59, 98, 19, 52, 95, 88, 65],
[85, 76, 56, 72, 43, 79, 53, 37],
[74, 46, 95, 27, 81, 97, 93, 69],
[49, 46, 12, 83, 15, 63, 20, 79]])
输入行，col掩码-
In [20]: row_mask = np.array([0,1,1,0,0,1,0],dtype=bool)
In [21]: col_mask = np.array([1,0,1,0,1,1,0,0],dtype=bool)
做出选择-
In [22]: x[np.ix_(row_mask,col_mask)]
Out[22]:
array([[88, 46, 44, 81],
[31, 47, 52, 15],
[74, 95, 81, 97]])
使用标量进行分配-
In [23]: x[np.ix_(row_mask,col_mask)] = -1
In [24]: x
Out[24]:
array([[17, 39, 88, 14, 73, 58, 17, 78],
[-1, 92, -1, 67, -1, -1, 17, 67],
[-1, 70, -1, 90, -1, -1, 24, 22],
[19, 59, 98, 19, 52, 95, 88, 65],
[85, 76, 56, 72, 43, 79, 53, 37],
[-1, 46, -1, 27, -1, -1, 93, 69],
[49, 46, 12, 83, 15, 63, 20, 79]])
使用2D块(可广播数组)进行分配-
Make assignments with 2D block(broadcastable array) -
In [25]: rand_arr = -np.arange(12).reshape(3,4)
In [26]: x[np.ix_(row_mask,col_mask)] = rand_arr
In [27]: x
Out[27]:
array([[ 17, 39, 88, 14, 73, 58, 17, 78],
[ 0, 92, -1, 67, -2, -3, 17, 67],
[ -4, 70, -5, 90, -6, -7, 24, 22],
[ 19, 59, 98, 19, 52, 95, 88, 65],
[ 85, 76, 56, 72, 43, 79, 53, 37],
[ -8, 46, -9, 27, -10, -11, 93, 69],
[ 49, 46, 12, 83, 15, 63, 20, 79]])
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