将2D数组复制到第3维,N次(Python) [英] copy 2D array into 3rd dimension, N times (Python)
问题描述
我想将一个numpy的2D数组复制到第三维.例如,给定(2D)numpy数组:
I'd like to copy a numpy 2D array into a third dimension. For example, given the (2D) numpy array:
import numpy as np
arr = np.array([[1,2],[1,2]])
# arr.shape = (2, 2)
将其转换为3D矩阵,并在一个新维度中包含N个此类副本.对N = 3的arr
起作用,输出应为:
convert it into a 3D matrix with N such copies in a new dimension. Acting on arr
with N=3, the output should be:
new_arr = np.array([[[1,2],[1,2]],[[1,2],[1,2]],[[1,2],[1,2]]])
# new_arr.shape = (3, 2, 2)
推荐答案
Probably the cleanest way is to use np.repeat
:
a = np.array([[1, 2], [1, 2]])
print(a.shape)
# (2, 2)
# indexing with np.newaxis inserts a new 3rd dimension, which we then repeat the
# array along, (you can achieve the same effect by indexing with None, see below)
b = np.repeat(a[:, :, np.newaxis], 3, axis=2)
print(b.shape)
# (2, 2, 3)
print(b[:, :, 0])
# [[1 2]
# [1 2]]
print(b[:, :, 1])
# [[1 2]
# [1 2]]
print(b[:, :, 2])
# [[1 2]
# [1 2]]
话虽如此,通过使用广播.例如,假设我要添加一个(3,)
向量:
Having said that, you can often avoid repeating your arrays altogether by using broadcasting. For example, let's say I wanted to add a (3,)
vector:
c = np.array([1, 2, 3])
到a
.我可以在第三维中复制a
的内容3次,然后在第一维和第二维中复制c
的内容两次,这样我的两个数组都是(2, 2, 3)
,然后计算它们的总和.但是,这样做更加简单快捷:
to a
. I could copy the contents of a
3 times in the third dimension, then copy the contents of c
twice in both the first and second dimensions, so that both of my arrays were (2, 2, 3)
, then compute their sum. However, it's much simpler and quicker to do this:
d = a[..., None] + c[None, None, :]
在这里,a[..., None]
具有形状(2, 2, 1)
,而c[None, None, :]
具有形状(1, 1, 3)
*.当我计算总和时,结果沿大小为1的维度广播"出去,结果为形状为(2, 2, 3)
:
Here, a[..., None]
has shape (2, 2, 1)
and c[None, None, :]
has shape (1, 1, 3)
*. When I compute the sum, the result gets 'broadcast' out along the dimensions of size 1, giving me a result of shape (2, 2, 3)
:
print(d.shape)
# (2, 2, 3)
print(d[..., 0]) # a + c[0]
# [[2 3]
# [2 3]]
print(d[..., 1]) # a + c[1]
# [[3 4]
# [3 4]]
print(d[..., 2]) # a + c[2]
# [[4 5]
# [4 5]]
广播是一种非常强大的技术,因为它避免了在内存中创建输入数组的重复副本所涉及的额外开销.
Broadcasting is a very powerful technique because it avoids the additional overhead involved in creating repeated copies of your input arrays in memory.
*尽管为清楚起见我将它们包括在内,但实际上并不需要None
到c
的索引-您也可以执行a[..., None] + c
,即针对(3,)
数组广播(2, 2, 1)
数组.这是因为,如果其中一个数组的维数小于另一个数组的维数,则仅两个数组的 trailing 维度需要兼容.举一个更复杂的例子:
* Although I included them for clarity, the None
indices into c
aren't actually necessary - you could also do a[..., None] + c
, i.e. broadcast a (2, 2, 1)
array against a (3,)
array. This is because if one of the arrays has fewer dimensions than the other then only the trailing dimensions of the two arrays need to be compatible. To give a more complicated example:
a = np.ones((6, 1, 4, 3, 1)) # 6 x 1 x 4 x 3 x 1
b = np.ones((5, 1, 3, 2)) # 5 x 1 x 3 x 2
result = a + b # 6 x 5 x 4 x 3 x 2
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