How to standardize matrix row-wise (axis=1)?

Question

For a two-dimensional array, I'm trying to make a standardize-function, which should work row-wise and column-wise. I'm not sure what to do when an argument is given with axis=1 (row-wise).

def standardize(x, axis=None):
if axis == 0:
    return (x - x.mean(axis)) / x.std(axis)
else:
    ?????

I tried to change axis to axis = 1 in this part: (x - x.mean(axis)) / x.std(axis)

But then I got the following error:

 ValueError: operands could not be broadcast together with shapes (4,3) (4,)

Can someone explain to me what to do as I'm still a beginner?

Answer 1

The reason for the error you are seeing is that you cannot calculate

x - x.mean(1)

because

x.shape = (4, 3)
x.mean(1).shape = (4,)  # mean(), sum(), std() etc. remove the dimension they are applied to

However, you could do the operation if we could somehow make sure mean() keeps the dimension it is applied to, resulting in

x.mean(1).shape = (4, 1)

(look up NumPy Broadcasting rules).

Because this is such a common issue, the NumPy developers introduced a parameter that does exactly that: keepdims=True, which you should use in mean() and std():

def standardize(x, axis=None):
    return (x - x.mean(axis, keepdims=True)) / x.std(axis, keepdims=True)