import numpy as np

One dimensional indexing¶

x = np.arange(10)
x

array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])

x[5]

5

x[5:8]

array([5, 6, 7])

x[5:8] = 12

x

array([ 0,  1,  2,  3,  4, 12, 12, 12,  8,  9])

Memory model

Slice of an array is a view. Modifications to the slice will modify the underlying array.

x_slice = x[5:8]
x_slice

array([12, 12, 12])

x_slice[-1] = -100
x_slice

array([  12,   12, -100])

x

array([   0,    1,    2,    3,    4,   12,   12, -100,    8,    9])

Multi-dimensional indexing¶

y = np.array([[1,2,3],
              [4,5,6],
              [7,8,9]])
y

array([[1, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])

There are two dimensions, so we need two indices to get a single entry in the matrix.

y[0][2]

3

y[0, 2]

3

We can get an entire row:

$y[i]$ is the $i$-th row.
$y[i,:]$ is equivalent. This is preferred.
- Fix the row to $i$,
- Allow the column to be anything.

y[0]

array([1, 2, 3])

y[0,:]

array([1, 2, 3])

We can get an entire column.

$y[:, i]$ is the $i$-th column.
- Allow the row to be anything.
- Fix the column to $j$.

y[:, 2]

array([3, 6, 9])

The general syntax of slicing along a dimension.

i:j: from $i$ to $j-1$ inclusive.
:j : from $0$ to $j-1$ inclusive.
i: : from $i$ to the last index in the dimension.
i:j:k: from $i$ to $j-1$ inclusive, and skip with step size $k$: $i$, $i+k$, $i+2k$, $\dots$
$[i,j,k,\dots]$: only indices that are included in the list

y[0:2, 2]

array([3, 6])

y[0:, 2]

array([3, 6, 9])

y[:2, 2]

array([3, 6])

y[:2, :2]

array([[1, 2],
       [4, 5]])

y[:,[2,1,0]]

array([[3, 2, 1],
       [6, 5, 4],
       [9, 8, 7]])

y[:,2::-1]

array([[3, 2, 1],
       [6, 5, 4],
       [9, 8, 7]])

y[1:2, :2]

array([[4, 5]])

Note:

Observe y[1:2, :2] is not the same as y[1,:2].