one-dimensional array shapes (length,) vs. (length,1) vs. (length)

Question

When I check the shape of an array using numpy.shape(), I sometimes get (length,1) and sometimes (length,). It looks like the difference is a column vs. row vector... but It doesn't seem like that changes anything about the array itself [except some functions complain when I pass an array with shape (length,1)].

What is the difference between these two?
Why isn't the shape just, (length)?

Answer 1

The point is that say a vector can be seen either as

• a vector
• a matrix with only one column
• a 3 dimensional array where the 2nd and 3rd dimensions have length one
• ...

You can add dimensions using [:, np.newaxis] syntax or drop dimensions using np.squeeze:

>>> xs = np.array([1, 2, 3, 4, 5])
>>> xs.shape
(5,)
>>> xs[:, np.newaxis].shape  # a matrix with only one column
(5, 1)
>>> xs[np.newaxis, :].shape  # a matrix with only one row
(1, 5)
>>> xs[:, np.newaxis, np.newaxis].shape  # a 3 dimensional array
(5, 1, 1)
>>> np.squeeze(xs[:, np.newaxis, np.newaxis]).shape
(5,)