Dimensional Indexing

Numpy support an extremely powerful tool - Indexing dimensions.

To index dimension we use the colon :. the colon takes all of the elements at the specific index it is placed. For example assume we have an array with the shape ary.shape # --> (2, 1, 3, 1), placing the colon : at ary[:, 0, 0, 0] will take the two left most elements of the shape and for each one of these it will extract the zeroth element for the rest of dimensions.

Note: The location of the colon at the brackets [] is the dimension we are indexing, meaning

• ary[:, 0, 0, 0] Index the 4D dimension
• ary[0, :, 0, 0] Index the 3D dimension
• ary[0, 0, :, 0] Index the 2D dimension
• ary[0, 0, 0, :] Index the 1D dimension
• ary[:, :, 0, 0] Index the 4D and the 3D dimensions
• etc

Example 1

ary = np.array([
	[1, 2], 
	[3, 4]
])
ary[:, 0] # --> [1, 3]
ary[0, :] # --> [1, 2]

The colon takes all of the elements at the specified index and continues to the next index

In our case: 

• ary[:, 0] We take all the first elements and at each element we take the 0 element
• ary[0, :] We take the first element and at the element we take all elements.

Exmaple 2

3D array

ary = np.array([
	[[1, 2], [3, 4]],
	[[5, 6], [7, 8]]
])
ary[:, 0, :] # --> [[1, 2], [5, 6]]
ary[:, :, 0] # --> [[1, 3], [5, 7]]

• ary[:, 0, :] We take all the elements, then we take the first element and at last we take everything there
• ary[:, :, 0] We take all the elements, then we take all of these elements and at last we take the first element at each.
• Can you guess what is the output for ary[0, :, :]

Exmaple 3

Get the first and last index from every row

x = np.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],
])
x[:, np.array([0, -1])]
>>> [0, 5, 6, 11, 12, 17, 18, 23]

Example 4

An array with the shape (2, 1, 3, 1) just like in the opening example

ary = np.array([
    [
        [
            [1],[2],[3]
        ]
    ],
    [
        [
            [4],[5],[6]
        ]
    ]
])
ary[:, 0, 0, 0] # --> [1, 4]
ary[0, :, 0, 0] # --> [1]
ary[0, 0, :, 0] # --> [1, 2, 3]
ary[0, 0, 0, :] # --> [1]

Note: it is possible to use the slicing syntax: start:stop:step we learned at the Slicing lesson as well

• ary[:, 0:5, 2:3, :]