TL;DR

This visual example will show you how to a neatly select elements in a NumPy Matrix (2 dimensional array) in a pretty entertaining way (I promise).

(Caution: this is a NumPy array specific example with the aim of illustrating the a use case of “double colons” :: for jumping of elements in multiple axes. This example does not cover native Python data structures like List).

One concrete example to rule them all…

Say we have a NumPy matrix that looks like this:

    In [1]: import numpy as np

    In [2]: X = np.arange(100).reshape(10,10)

    In [3]: X
    Out[3]:
    array([[ 0,  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]])

Say for some reason, your boss wants you to select the following elements:

“But How???”… Read on! (We can do this in a 2-step approach)

Step 1 – Obtain subset

Specify the “start index” and “end index” in both row-wise and column-wise directions.

In code:

    In [5]: X2 = X[2:9,3:8]

    In [6]: X2
    Out[6]:
    array([[23, 24, 25, 26, 27],
           [33, 34, 35, 36, 37],
           [43, 44, 45, 46, 47],
           [53, 54, 55, 56, 57],
           [63, 64, 65, 66, 67],
           [73, 74, 75, 76, 77],
           [83, 84, 85, 86, 87]])

Notice now we’ve just obtained our subset, with the use of simple start and end indexing technique. Next up, how to do that “jumping”… (read on!)

Step 2 – Select elements (with the “jump step” argument)

We can now specify the “jump steps” in both row-wise and column-wise directions (to select elements in a “jumping” way) like this:

In code (note the double colons):

    In [7]: X3 = X2[::3, ::2]

    In [8]: X3
    Out[8]:
    array([[23, 25, 27],
           [53, 55, 57],
           [83, 85, 87]])

We have just selected all the elements as required! :)

Consolidate Step 1 (start and end) and Step 2 (“jumping”)

Now we know the concept, we can easily combine step 1 and step 2 into one consolidated step – for compactness:

    In [9]: X4 = X[2:9,3:8][::3,::2]

        In [10]: X4
        Out[10]:
        array([[23, 25, 27],
               [53, 55, 57],
               [83, 85, 87]])

Done!

(I’ve also posted this trick in this Stackoverflow forum)