Question! about cs231n-2017

[Burton2000]

The quick answer is so the variables can broadcast correctly so we can actually add them together. If you were to also add a new axis to Y_squared you then have 2 numpy arrays with different shapes that numpy can not add together.

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The longer answer is:

X_squared has shape: (num_test, )
Y_squared has shape: (num_train, )
XY has shape: (num_test, num_train)

We add a new axis to X_squared.
X_squared now has shape (num_test, 1)

Numpy will now let you add X_squared and Y_squared because of its broadcasting rules.

You can think of what happens during broadcasting as 'stretching' X_squared along the axis we just added to make it num_train in length. Numpy will then apply the add operation across all the rows (i.e. Y_squared will be added to each row of the 'stretched' X_squared ).

Instead of adding a new axis to X_squared we could have added a new axis to Y_squared and broadcasting would have allowed this. But, the shape coming out would be (num_train, num_test) which would not add to XY which has shape (num_test, num_train). Because of this we know we must add the new axis to X_squared.

Let me know if that explains it to you, for more info look here:
https://docs.scipy.org/doc/numpy/user/basics.broadcasting.html
https://medium.com/dataholiks-distillery/l2-distance-matrix-vectorization-trick-26aa3247ac6c
https://stackoverflow.com/questions/31587802/numpy-add-a-vector-to-matrix-column-wise

[cucrui]

really useful,thanks bro!