To illustrate indexing, let's first create an array with random data using the following command:

import numpy.random
a = np.random.rand(6,5)
print a

This creates an array of dimension (6,5) that contains random data. Individual elements of the array are accessed with the usual index notation, for example, a[2,4].

An important technique to manipulate data in NumPy is the use of slices. A slice can be thought of as a subarray of an array. For example, let's say we want to extract a subarray with the middle two rows and first two columns of the array a. Consider the following command lines:

b = a[2:4,0:2]
print b

Now, let's make a very important observation. A slice is simply a view of an array, and no data is actually copied. This can be seen by running the following commands:

b[0,0]=0
print a

So, changes in b affect the array a! If we really need a copy, we need to explicitly say we want one. This can be done using the following command line:

c = np.copy(a[2:4,0:2])
c[0,0] = -1
print a

In the slice notation i:j, we can omit either i or j, in which case the slice refers to the beginning or end of the corresponding axis:

print a[:4,3:]

Omitting both i and j refers to a whole axis:

print a[:,2:4]

Finally, we can use the notation i:j:k to specify a stride k in the slice. In the following example, we first create a larger random array to illustrate this:

a = np.random.rand(10,6)
print a
print
print a[1:7:2,5:0:-3]

Let's now consider slices of higher dimensional arrays. We will start by creating a really large three-dimensional array as follows:

d1, d2, d3 = 4, 5, 3
a = np.random.rand(d1, d2, d3)
print a

Suppose we want to extract all elements with index 1 in the last axis. This can be done easily using an ellipsis object as follows:

print a[...,1]

The preceding command line is equivalent to the following one:

print a[:,:,1]

It is also possible to augment the matrix along an axis when slicing, as follows:

print a[0, :, np.newaxis, 0]

Compare the output of the preceding command line with the output of the following:

print a[0, :, 0]