What is the role of keepdims in Numpy (Python)?

Question

When I use np.sum, I encountered a parameter called keepdims. After looking up the docs, I still cannot understand the meaning of keepdims.

keepdims: bool, optional

If this is set to True, the axes which are reduced are left in the result as dimensions with size one. With this option, the result will broadcast correctly against the original arr.

I will appreciate it if anyone can make some sense of this with a simple example.

Answer 1

Consider a small 2d array:

In [180]: A=np.arange(12).reshape(3,4)
In [181]: A
Out[181]: 
array([[ 0,  1,  2,  3],
       [ 4,  5,  6,  7],
       [ 8,  9, 10, 11]])

Sum across rows; the result is a (3,) array

In [182]: A.sum(axis=1)
Out[182]: array([ 6, 22, 38])

But to sum (or divide) A by the sum requires reshaping

In [183]: A-A.sum(axis=1)
...
ValueError: operands could not be broadcast together with shapes (3,4) (3,) 
In [184]: A-A.sum(axis=1)[:,None]   # turn sum into (3,1)
Out[184]: 
array([[ -6,  -5,  -4,  -3],
       [-18, -17, -16, -15],
       [-30, -29, -28, -27]])

If I use keepdims, "the result will broadcast correctly against" A.

In [185]: A.sum(axis=1, keepdims=True)   # (3,1) array
Out[185]: 
array([[ 6],
       [22],
       [38]])
In [186]: A-A.sum(axis=1, keepdims=True)
Out[186]: 
array([[ -6,  -5,  -4,  -3],
       [-18, -17, -16, -15],
       [-30, -29, -28, -27]])

If I sum the other way, I don't need the keepdims. Broadcasting this sum is automatic: A.sum(axis=0)[None,:]. But there's no harm in using keepdims.

In [190]: A.sum(axis=0)
Out[190]: array([12, 15, 18, 21])    # (4,)
In [191]: A-A.sum(axis=0)
Out[191]: 
array([[-12, -14, -16, -18],
       [ -8, -10, -12, -14],
       [ -4,  -6,  -8, -10]])

If you prefer, these actions might make more sense with np.mean, normalizing the array over columns or rows. In any case it can simplify further math between the original array and the sum/mean.