Numpy Sum Axis Intuition

Typical Axis Order Example: [Batch, Height, Width, Feature]

I’ve always thought that axis 0 is row-wise, and axis 1 is column-wise.

 row-wise (axis 0) --->  [[ 0  1]   
                          [ 0  5]]  
                            ⭡
                           column-wise (axis 1)

However, what numpy.sum gives me is the exact opposite of what I thought it would be.

>>> np.sum([[0, 1], [0, 5]], axis=0)
array([0, 6])

>>> np.sum([[0, 1], [0, 5]], axis=1)
array([1, 5])

So what’s going on here? Am I the only one who is wondering this?

The way to understand what “axis” means in numpy sum is that it collapses the specified axis. So when it collapses the axis 0 (the row), it becomes just one row (it sums column-wise).

Why did numpy choose to act this way?

It is possible that this might be confusing when discussing 2-d arrays; however, when discussing 3-d, 4-d, n-d arrays, this is a more straightforward way to define the axis.

# Let's experiment with 3-d array.
  
In [5]: x = np.array([[[1,2],[3,4]],[[1,2],[3,4]]])

In [6]: x
Out[6]: 
array([[[1, 2],
        [3, 4]],

       [[1, 2],
        [3, 4]]])

In [7]: x.shape
Out[7]: (2, 2, 2)

In [8]: x[0]        # axis-0
Out[8]: 
array([[1, 2],
       [3, 4]])

In [9]: x[1]        # still axis-0
Out[9]: 
array([[1, 2],
       [3, 4]])

In [10]: x[0][0]    # axis-1
Out[10]: array([1, 2])

In [11]: x[0][0][0] # axis-2
Out[11]: 1

In [12]: np.sum(x, axis=0)  # Notice that it eliminated the specified axis.
Out[12]: 
array([[2, 4],
       [6, 8]])

In [13]: np.sum(x, axis=1)
Out[13]: 
array([[4, 6],
       [4, 6]])

In [14]: np.sum(x, axis=2)
Out[14]: 
array([[3, 7],
       [3, 7]])

The same logic goes for Tensorflow.

t1 = [[1, 2, 3], [4, 5, 6]]
t2 = [[7, 8, 9], [10, 11, 12]]

tf.concat([t1, t2], 0)  # [[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]]
tf.concat([t1, t2], 1)  # [[1, 2, 3, 7, 8, 9], [4, 5, 6, 10, 11, 12]]

# tensor t3 with shape [2, 3]
# tensor t4 with shape [2, 3]
tf.shape(tf.concat([t3, t4], 0))  # [4, 3]
tf.shape(tf.concat([t3, t4], 1))  # [2, 6]

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