Numpy reshape with negative values [duplicate]

Question

I'm really new to the numpy and currently confused with negative values in reshape.

import numpy as np

a=np.arange(6)
c=a.reshape(1,3,2)
d=a.reshape(-1,3,2)
e=a.reshape(-1,1,2)
print c
print
print d
print
print e

and it returns

[[[0 1]
  [2 3]
  [4 5]]]

[[[0 1]
  [2 3]
  [4 5]]]

[[[0 1]]

 [[2 3]]

 [[4 5]]]

The question here is that when comparing c and d, there's no difference at all. However in e, additional empty line is formed between each row. So, what exactly does the -1 do in reshape function, and why it causes empty lines between each row in e? Thanks !

Answer 1

When you add -1 to an axis in numpy it will just put everything else in that axis. This is, for an array a of shape (10, 10), the following operations will apply:

>>> a.reshape(-1, 10, 10) # a is (1, 10, 10)
>>> a.reshape( 1, 10, 10) # a is also (1, 10, 10)
>>> a.reshape(-1, 5, 5)   # a is (4, 5, 5), since 4 * 5 *  5 = 100
>>> a.reshape(-1, 5, 10)  # a is (2, 5, 10) since 2 * 5 * 10 = 100 

This is, when reshaping the total number of elements must be the same, so adding -1 to the shape just lets numpy calculate the remaining value for you, so that the product of the axes still matches the previous number of elements.

Answer 2

The difference between c and e is not only the additional space, but also the additional bracket around each pair, i.e.

[2 3]    vs    [[2 3]]

This is because the shape of c is [1, 3, 2], while the shape of e is [3, 1, 2]. The shape of d is also [1, 3, 2], and that is why c and d are equal.

When you put -1 in the shape, numpy infers it from the other dimensions, that is replaces -1 with product of all dimensions of a / product of all specified shapes