Why doesn't the Python 2D array index order matter when used with colon ( : )

Question

Creating a 2D array such as

x = [range(i, i+10) for i in xrange(1,100,10)]

and indexing using the colon operator like this

>>> x[2][:]
[21, 22, 23, 24, 25, 26, 27, 28, 29, 30]

works as expected. It returns all of row 2.

However, if I want to retrieve all of column 2, I would instinctively do

>>> x[:][2]

But this also returns

[21, 22, 23, 24, 25, 26, 27, 28, 29, 30]

What is the reasoning behind this? I would intuitively think that this returns the column 2 of each row.

(Also, I am aware I can use numpy to do x[:,2] or I could use list comprehensions to accomplish this, that's not my question)

Answer 1

x[2][:] will return the 3rd row of your array, and then return all elements inside that row.

x[:][2] will return all the rows of your array, and then return the 3rd row of them all.

Effectively, they're both the same, x[2][:] == x[:][2].

Printing them in the console it's obvious why this occurs:

In [138]: x[2]
Out[138]: [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]

In [139]: x[2][:]
Out[139]: [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]

In [140]: x[:]
Out[140]:
[[1, 2, 3, 4, 5, 6, 7, 8, 9, 10],
 [11, 12, 13, 14, 15, 16, 17, 18, 19, 20],
 [21, 22, 23, 24, 25, 26, 27, 28, 29, 30],
 [31, 32, 33, 34, 35, 36, 37, 38, 39, 40],
 [41, 42, 43, 44, 45, 46, 47, 48, 49, 50],
 [51, 52, 53, 54, 55, 56, 57, 58, 59, 60],
 [61, 62, 63, 64, 65, 66, 67, 68, 69, 70],
 [71, 72, 73, 74, 75, 76, 77, 78, 79, 80],
 [81, 82, 83, 84, 85, 86, 87, 88, 89, 90],
 [91, 92, 93, 94, 95, 96, 97, 98, 99, 100]]

In [141]: x[:][2]
Out[141]: [21, 22, 23, 24, 25, 26, 27, 28, 29, 30]

If you wish to get the columns then you can effectively transpose the lists using list(zip(*x)) (added the list in for Py 3). You could then do:

In [3]: list(zip(*x))[2]
Out[3]: (3, 13, 23, 33, 43, 53, 63, 73, 83, 93)

That aside, I'd suggest you use numpy instead for this kind of work.

Answer 2

The reason is that [:] just means "everything", and that the two indexing operations in a row are completely independent.

y = x[2][:]

is

tmp = x[2]
y = tmp[:]  # this only makes a copy, does nothing else

Similarly,

y = x[:][2]

is

tmp = x[:]  # this only makes a copy, does nothing else
y = tmp[2]

in effect both just mean

y = x[2]

There is no 2D indexing going on at any point, Python doesn't have 2D indexing (although numpy has hacks that make it work like there is actual 2D indexing going on).