[英]Slicing n-dimensional numpy array using list of indices
Say I have a 3 dimensional numpy array: 说我有一个3维numpy数组:
np.random.seed(1145)
A = np.random.random((5,5,5))
and I have two lists of indices corresponding to the 2nd and 3rd dimensions: 我有两个对应于第二和第三维度的索引列表:
second = [1,2]
third = [3,4]
and I want to select the elements in the numpy array corresponding to 我想选择numpy数组中对应的元素
A[:][second][third]
so the shape of the sliced array would be (5,2,2)
and 所以切片阵列的形状为(5,2,2)
和
A[:][second][third].flatten()
would be equivalent to to: 相当于:
In [226]:
for i in range(5):
for j in second:
for k in third:
print A[i][j][k]
0.556091074129
0.622016249651
0.622530505868
0.914954716368
0.729005532319
0.253214472335
0.892869371179
0.98279375528
0.814240066639
0.986060321906
0.829987410941
0.776715489939
0.404772469431
0.204696635072
0.190891168574
0.869554447412
0.364076117846
0.04760811817
0.440210532601
0.981601369658
Is there a way to slice a numpy array in this way? 有没有办法以这种方式切割numpy数组? So far when I try A[:][second][third]
I get IndexError: index 3 is out of bounds for axis 0 with size 2
because the [:]
for the first dimension seems to be ignored. 到目前为止,当我尝试A[:][second][third]
我得到IndexError: index 3 is out of bounds for axis 0 with size 2
因为第一维的[:]
似乎被忽略了。
Numpy uses multiple indexing, so instead of A[1][2][3]
, you can--and should--use A[1,2,3]
. Numpy使用多个索引,因此您可以 - 而且应该 - 使用A[1,2,3]
而不是A[1][2][3]
A[1,2,3]
。
You might then think you could do A[:, second, third]
, but the numpy indices are broadcast , and broadcasting second
and third
(two one-dimensional sequences) ends up being the numpy equivalent of zip
, so the result has shape (5, 2)
. 你可能认为你可以做A[:, second, third]
,但是numpy索引是广播的 ,广播second
和third
(两个一维序列)最终是zip
的numpy等价物,所以结果有形(5, 2)
。
What you really want is to index with, in effect, the outer product of second
and third
. 你真正想要的是实际上用second
和third
的外积进行索引。 You can do this with broadcasting by making one of them, say second
into a two-dimensional array with shape (2,1). 您可以通过其中的一个与广播做到这一点,说second
与形状(2,1)二维数组。 Then the shape that results from broadcasting second
and third
together is (2,2)
. 然后,由second
和third
广播一起产生的形状是(2,2)
。
For example: 例如:
In [8]: import numpy as np
In [9]: a = np.arange(125).reshape(5,5,5)
In [10]: second = [1,2]
In [11]: third = [3,4]
In [12]: s = a[:, np.array(second).reshape(-1,1), third]
In [13]: s.shape
Out[13]: (5, 2, 2)
Note that, in this specific example, the values in second
and third
are sequential. 注意,在该具体示例中, second
和third
中的值是顺序的。 If that is typical, you can simply use slices: 如果这是典型的,您可以简单地使用切片:
In [14]: s2 = a[:, 1:3, 3:5]
In [15]: s2.shape
Out[15]: (5, 2, 2)
In [16]: np.all(s == s2)
Out[16]: True
There are a couple very important difference in those two methods. 这两种方法有一些非常重要的区别。
second = [0, 2, 3]
. 例如,如果second = [0, 2, 3]
,它将起作用。 (Sometimes you'll see this style of indexing referred to as "fancy indexing".) (有时你会看到这种索引方式被称为“花式索引”。) s2
is a view into the same block of memory used by a
. 在第二种方法(仅使用切片),阵列s2
是一个视图到由所使用的存储器中的相同块a
。 An in-place change in one will change them both. 一个就地改变将改变它们。 One way would be to use np.ix_
: 一种方法是使用np.ix_
:
>>> out = A[np.ix_(range(A.shape[0]),second, third)]
>>> out.shape
(5, 2, 2)
>>> manual = [A[i,j,k] for i in range(5) for j in second for k in third]
>>> (out.ravel() == manual).all()
True
Downside is that you have to specify the missing coordinate ranges explicitly, but you could wrap that into a function. 缺点是您必须明确指定缺少的坐标范围,但您可以将其包装到函数中。
I think there are three problems with your approach: 我认为你的方法有三个问题:
second
and third
should be slices
second
和third
都应该是slices
1
to 3
and from 3
to 5
由于'to'索引是独占的,因此它们应该从1
到3
,从3
到5
A[:][second][third]
, you should use A[:,second,third]
而不是A[:][second][third]
,你应该使用A[:,second,third]
Try this: 试试这个:
>>> np.random.seed(1145)
>>> A = np.random.random((5,5,5))
>>> second = slice(1,3)
>>> third = slice(3,5)
>>> A[:,second,third].shape
(5, 2, 2)
>>> A[:,second,third].flatten()
array([ 0.43285482, 0.80820122, 0.64878266, 0.62689481, 0.01298507,
0.42112921, 0.23104051, 0.34601169, 0.24838564, 0.66162209,
0.96115751, 0.07338851, 0.33109539, 0.55168356, 0.33925748,
0.2353348 , 0.91254398, 0.44692211, 0.60975602, 0.64610556])
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