如何将二维数组复制到第三维，N 次? [英] How to copy a 2D array into a 3rd dimension, N times?

问题描述

我想将一个 numpy 二维数组复制到第三维中.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)

将其转换为在新维度中具有 N 个此类副本的 3D 矩阵.用N=3作用于arr，输出应该是:

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

可能最干净的方法是使用 np.repeat:

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]]

<小时>

话虽如此，您通常可以通过使用 广播.例如，假设我想添加一个 (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，这样做更简单、更快捷:

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, :]

这里，a[..., None] 有形状 (2, 2, 1) 和 c[None, None, :]code> 的形状为 (1, 1, 3)*.当我计算总和时，结果沿着尺寸 1 的维度广播"出来，给我形状 (2, 2, 3) 的结果:

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.

* 尽管为了清楚起见我将它们包括在内，c 中的 None 索引实际上并不是必需的 - 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比另一个少，那么只有两个数组的尾随维数需要兼容.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

这篇关于如何将二维数组复制到第三维，N 次?的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！