Reshape and transpose

Reshape without changing the data

The reshape rearranges the same elements into another form. The total needs to remain the same: it never creates or removes elements. And the -1 in one of the dimensions means "calculate yourself":

import numpy as np

arr = np.arange(12)
print(arr.reshape(3, 4))
print(arr.reshape(2, -1).shape, arr.reshape(-1, 3).shape)
try:
    arr.reshape(5, 3)
except ValueError as erro:
    print(erro)

[[ 0  1  2  3]
 [ 4  5  6  7]
 [ 8  9 10 11]]
(2, 6) (4, 3)
cannot reshape array of size 12 into shape (5,3)

Five times three equals 15, and the array has 12 elements, so NumPy refuses. The reshape(2, -1) figured out on its own that the second dimension is 6.

Transpose, flatten, and insert axes

grade = np.arange(6).reshape(2, 3)
print(grade.T.shape, grade.transpose().shape)
print(grade.flatten(), grade.ravel())
print(grade[:, np.newaxis, :].shape, grade[..., None].shape)
print(np.squeeze(np.zeros((1, 3, 1))).shape)

(3, 2) (3, 2)
[0 1 2 3 4 5] [0 1 2 3 4 5]
(2, 1, 3) (2, 3, 1)
(3,)

The difference between flatten and ravel is the same as in the previous chapter: one copies, the other shares memory, and changing the result of ravel changes the original:

r = grade.ravel()
r[0] = 99
print(grade[0, 0])
f = grade.flatten()
f[0] = -1
print(grade[0, 0])

99
99

The extra axis trick

Inserting an axis of size 1 is the way to prepare an array for the broadcasting of the next chapter. An array of shape (3,) becomes a column (3, 1) with reshape(-1, 1) or with [:, None]:

vetor = np.array([1, 2, 3])
print(vetor.reshape(-1, 1))

[[1]
 [2]
 [3]]

A real case: batch of images

A batch of 10 images of 28 by 28 pixels has shape (10, 28, 28). Many models expect each image as a vector of 784 numbers, that is, shape (10, 784). The -1 calculates the 784 by itself:

lote = np.zeros((10, 28, 28))
print(lote.reshape(10, -1).shape)

(10, 784)

reshape returns a view when it can

The reshape returns a view if memory allows and only copies when there is no other way. Therefore, after a reshape, keep in mind that changing the result can change the original. If in doubt, check with np.shares_memory.