Python Numpy 的 sum 函数中的 axis = 0 有什么作用？

What does axis = 0 do in Numpy's sum function?

提问by Bishwajit Purkaystha

I am learning Python, and have encountered numpy.sum. It has an optional parameter axis. This parameter is used to get either column-wise summation or row-wise summation. When axis = 0we imply to sum it over columns only. For example,

我正在学习 Python，并且遇到过numpy.sum. 它有一个可选参数axis。此参数用于获得按列求和或按行求和。当axis = 0我们暗示仅对列求和时。例如，

a = np.array([[1, 2, 3], [4, 5, 6]])
np.sum(a, axis = 0)

This snippet of code produces output: array([5, 7, 9]), fine. But if I do:

这段代码产生输出：array([5, 7, 9])，很好。但如果我这样做：

a = np.array([1, 2, 3])
np.sum(a, axis = 0)

I get result: 6, why is that? Shouldn't I get array([1, 2, 3])?

我得到结果：6，为什么？我不应该得到array([1, 2, 3])吗？

回答by debaonline4u

If someone need this visual description:

如果有人需要这个视觉描述：

回答by juanpa.arrivillaga

All that is going on is that numpy is summing across the first (0th) and only axis. Consider the following:

所发生的一切是 numpy 在第一个（第 0 个）也是唯一一个轴上求和。考虑以下：

In [2]: a = np.array([1, 2, 3])

In [3]: a.shape
Out[3]: (3,)

In [4]: len(a.shape) # number of dimensions
Out[4]: 1

In [5]: a1 = a.reshape(3,1)

In [6]: a2 = a.reshape(1,3)

In [7]: a1
Out[7]: 
array([[1],
       [2],
       [3]])

In [8]: a2
Out[8]: array([[1, 2, 3]])

In [9]: a1.sum(axis=1)
Out[9]: array([1, 2, 3])

In [10]: a1.sum(axis=0)
Out[10]: array([6])

In [11]: a2.sum(axis=1)
Out[11]: array([6])

In [12]: a2.sum(axis=0)
Out[12]: array([1, 2, 3])

So, to be more explicit:

所以，更明确地说：

In [15]: a1.shape
Out[15]: (3, 1)

a1is 2-dimensional, the "long" axis being the first.

a1是二维的，“长”轴是第一个。

In [16]: a1[:,0] # give me everything in the first axis, and the first part of the second
Out[16]: array([1, 2, 3])

Now, sum along the first axis:

现在，沿第一个轴求和：

In [17]: a1.sum(axis=0)
Out[17]: array([6])

Now, consider a less trivial two-dimensional case:

现在，考虑一个不太重要的二维情况：

In [20]: b = np.array([[1,2,3],[4,5,6]])

In [21]: b
Out[21]: 
array([[1, 2, 3],
       [4, 5, 6]])

In [22]: b.shape
Out[22]: (2, 3)

The first axis is the "rows". Sum alongthe rows:

第一个轴是“行”。沿行求和：

In [23]: b.sum(axis=0)
Out[23]: array([5, 7, 9])

The second axis are the "columns". Sum alongthe columns:

第二个轴是“列”。沿列求和：

In [24]: b.sum(axis=1)
Out[24]: array([ 6, 15])

回答by Apoorve

The axis i in np.sum(a, axis=i)is the ith index of the shape of that array (zero-indexed).

轴 i innp.sum(a, axis=i)是该数组形状的第 i 个索引（零索引）。

Let's try and understand what that means with some examples:

让我们试着用一些例子来理解这意味着什么：

a = np.array([1, 2, 3])
print (a.shape) #prints (3,) 
#so axis = 0 corresponds to 3 and axis = 1 corresponds to nothing

Let's see what axis = 0 and axis = 1 do to the sum:

让我们看看axis = 0和axis = 1对总和的作用：

sum = np.sum(a, axis=0) #sum = 6

So, sum = np.sum(a, axis=0)would sum up all numbers that the 0th index of a.shape refers to, which in this case are 3 numbers. Since numpy arrays are, by default, row-major (which is just another way of saying that the row index is specified before the column index), thus axis=0 would sum the three numbers that the shape refers to.

因此，sum = np.sum(a, axis=0)将总结 a.shape 的第 0 个索引所指的所有数字，在这种情况下是 3 个数字。由于默认情况下 numpy 数组是行优先的（这只是在列索引之前指定行索引的另一种说法），因此 axis=0 将对形状引用的三个数字求和。

sum = np.sum(a, axis=1) #gives an error

Similarly, np.sum(a, axis=1)should sum up all the numbers that the 1st index of np.shape refers to, but since there is no first index of the shape, we get an error.

同样，np.sum(a, axis=1)应该总结 np.shape 的第一个索引所指的所有数字，但由于没有形状的第一个索引，我们得到一个错误。

Let's take another example:

让我们再举一个例子：

b = np.array([[1,2,3],
             [4,5,6]])
print(b.shape) #prints (2,3)
#axis = 0 corresponds to 2 and axis = 1 corresponds to 3

And now, let's see what changing the axis does:

现在，让我们看看改变轴的作用：

sum = np.sum(b, axis=0) #sum = [5, 7, 9] of shape(3,)

We know that axis = 0 should sum along the first index of the shape and we expect it to find two numbers along this axis (by looking at the shape). So [1+4, 2+5, 3+6].

我们知道 axis = 0 应该沿着形状的第一个索引求和，我们期望它沿着这个轴找到两个数字（通过查看形状）。所以[1+4, 2+5, 3+6]。

sum = np.sum(b, axis=1) #sum = [6, 15] of shape(2,)

Now the sum is along axis = 1, and from the shape we can see this it is an axis along which there are 3 numbers to be summed. So, [1+2+3,4+5+6]

现在总和沿着轴 = 1，从形状我们可以看出这是一个轴，沿着轴有 3 个要求和的数字。所以，[1+2+3,4+5+6]

回答by Liang

axisis the index of array index. the array index starts from 0, counting from right to left.

axis是数组索引的索引。数组索引从 0 开始，从右到左计数。

hence, np.sum(a, axis = 0)means sum along the right most index.

因此， np.sum(a, axis = 0)意味着沿着最右边的索引求和。