Python Programming

Ah, I feel better squeezing that singleton dimension out of my system!

But wait… apparently the singleton dimension could be useful after all!

Mission 6: Put that lonely singleton back into the array

So now I have an ($M \times K \times N$) array called x.

And an ($M \times N$) array called y.

I need to add these two arrays, but unfortunately I cannot do so because their dimensions do not match!

>>> import numpy as np
>>> x = np.random.random_sample((10, 8, 5))
>>> y = np.random.random_sample((10, 5))
>>> print(x.shape)
(10, 8, 5)
>>> print(y.shape)
(10, 5)
>>> z = x + y
Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
ValueError: operands could not be broadcast together with shapes (10,8,5) (10,5)

I think y.reshape(10, 1, 5) can solve this. NumPy can then perform its array broadcasting magic to add x and y. But I find it a hassle having to explicitly specify the sizes of $M$ (10) and $N$ (5) each time. And they can change any time too! y.reshape(-1, 1, -1) will not work because there can at most be only one -1.

Is there an easier way to add a new singleton dimension to y?

This is your final mission to pass your probation. Help me find a better way to solve this issue!

Hint: A little bird told me that the answer can be found on this page in the official documentation

👀 Peek at sample solutions

>>> expanded_y = y[:, np.newaxis, :]
>>> print(expanded_y.shape)
(10, 1, 5)
>>> z = x + expanded_y

>>> expanded_y = y[:, None, :]
>>> print(expanded_y.shape)
(10, 1, 5)
>>> z = x + expanded_y

>>> expanded_y = np.expand_dims(y, axis=1)
>>> print(expanded_y.shape)
(10, 1, 5)

>>> expanded_y = y[np.newaxis, :, np.newaxis, np.newaxis, :]
>>> print(expanded_y.shape)
(1, 10, 1, 1, 5)

>>> x = np.array([1, 2, 3])
>>> y = np.array([[4, 5, 6]])
>>> print(x.shape)
(3, )
>>> print(y.shape)
(1, 3) 
>>> x_new = x[:, np.newaxis]
>>> print(x_new.shape)
(3, 1)
>>> print(x @ y)
[[ 4  5  6]
 [ 8 10 12]
 [12 15 18]