问题描述
我想了解一下ndarray.sum(axis =)的工作方式.我知道axis = 0用于列，而axis = 1用于行.但是在3维(3轴)的情况下，以下结果很难解释.
I want to understand how this ndarray.sum(axis=) works. I know that axis=0 is for columns and axis=1 is for rows.But in case of 3 dimensions(3 axes) its difficult to interpret below result.
arr = np.arange(0,30).reshape(2,3,5)
arr
Out[1]:
array([[[ 0, 1, 2, 3, 4],
[ 5, 6, 7, 8, 9],
[10, 11, 12, 13, 14]],
[[15, 16, 17, 18, 19],
[20, 21, 22, 23, 24],
[25, 26, 27, 28, 29]]])
arr.sum(axis=0)
Out[2]:
array([[15, 17, 19, 21, 23],
[25, 27, 29, 31, 33],
[35, 37, 39, 41, 43]])
arr.sum(axis=1)
Out[8]:
array([[15, 18, 21, 24, 27],
[60, 63, 66, 69, 72]])
arr.sum(axis=2)
Out[3]:
array([[ 10, 35, 60],
[ 85, 110, 135]])
在此示例中，形状为(2,3,5)的 3轴数组，共有3行5列.但是，如果我从整体上看这个数组，似乎只有两行(都带有3个数组元素).
Here in this example of 3 axes array of shape(2,3,5), there are 3 rows and 5 columns. But if i look at this array as whole, seems like only two rows (both with 3 array elements).
任何人都可以解释这个总和如何在3个或更多轴(维度)的数组上工作.
Can anyone please explain how this sum works on array of 3 or more axes(dimensions).
推荐答案
numpy将(2,3,5)数组显示为2个3x5数组的块(3行，5列).或称它们为飞机"(MATLAB会将其显示为5个2x3的块).
numpy displays a (2,3,5) array as 2 blocks of 3x5 arrays (3 rows, 5 columns). Or call them 'planes' (MATLAB would show it as 5 blocks of 2x3).
numpy显示还与嵌套列表匹配-两个子列表的列表；每个都有3个子列表.每个元素长5个元素.
The numpy display also matches a nested list - a list of two sublists; each with 3 sublists. Each of those is 5 elements long.
在3x5 2d情况下，轴0沿3维度求和，从而形成5个元素的数组.用英语对行间和"或沿行列和"的描述有些含糊.重点放在结果，形状变化以及要累加的值上，而不是描述上.
In the 3x5 2d case, axis 0 sums along the 3 dimension, resulting in a 5 element array. The descriptions 'sum over rows' or 'sum along colulmns' are a little vague in English. Focus on the results, the change in shape, and which values are being summed, not on the description.
回到3d情况:
使用axis=0，它沿第一个维度求和，有效地将其删除，剩下3x5的数组. 0+15=16, 1+16=17 etc.
With axis=0, it sums along the 1st dimension, effectively removing it, leaving us with a 3x5 array. 0+15=16, 1+16=17 etc.
轴1，压缩尺寸3尺寸，结果为2x5. 0+5+10=15, etc.
Axis 1, condenses the size 3 dimension, result is 2x5. 0+5+10=15, etc.
第2轴，压缩尺寸5尺寸，结果为2x3，sum((0,1,2,3,4))
Axis 2, condense the size 5 dimenson, result is 2x3, sum((0,1,2,3,4))
您的示例很好，因为这三个维度是不同的，并且更容易看出在求和过程中消除了哪个维度.
Your example is good, since the 3 dimensions are different, and it is easier to see which one was eliminated during the sum.
使用2d时会有一些歧义； 行总和"-表示行被删除或保留了吗?有了3d，就不会有歧义.如果axis = 0，则只能将其删除，而将其余的2个删除.
With 2d there's some ambiguity; 'sum over rows' - does that mean the rows are eliminated or retained? With 3d there's no ambiguity; with axis=0, you can only remove it, leaving the other 2.
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