NumPy Indexing and Selection

In this lecture we will discuss how to select elements or groups of elements from an array.

In [2]:
import numpy as np
In [3]:
#Creating sample array
arr = np.arange(0,11)
In [4]:
#Show
arr
Out[4]:
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10])

Bracket Indexing and Selection

The simplest way to pick one or some elements of an array looks very similar to python lists:

In [5]:
#Get a value at an index
arr[8]
Out[5]:
8
In [6]:
#Get values in a range
arr[1:5]
Out[6]:
array([1, 2, 3, 4])
In [7]:
#Get values in a range
arr[0:5]
Out[7]:
array([0, 1, 2, 3, 4])

Broadcasting

Numpy arrays differ from a normal Python list because of their ability to broadcast:

In [8]:
#Setting a value with index range (Broadcasting)
arr[0:5]=100

#Show
arr
Out[8]:
array([100, 100, 100, 100, 100,   5,   6,   7,   8,   9,  10])
In [9]:
# Reset array, we'll see why I had to reset in  a moment
arr = np.arange(0,11)

#Show
arr
Out[9]:
array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10])
In [10]:
#Important notes on Slices
slice_of_arr = arr[0:6]

#Show slice
slice_of_arr
Out[10]:
array([0, 1, 2, 3, 4, 5])
In [11]:
#Change Slice
slice_of_arr[:]=99

#Show Slice again
slice_of_arr
Out[11]:
array([99, 99, 99, 99, 99, 99])

Now note the changes also occur in our original array!

In [12]:
arr
Out[12]:
array([99, 99, 99, 99, 99, 99,  6,  7,  8,  9, 10])

Data is not copied, it's a view of the original array! This avoids memory problems!

In [13]:
#To get a copy, need to be explicit
arr_copy = arr.copy()

arr_copy
Out[13]:
array([99, 99, 99, 99, 99, 99,  6,  7,  8,  9, 10])

Indexing a 2D array (matrices)

The general format is arr_2d[row][col] or arr_2d[row,col]. I recommend usually using the comma notation for clarity.

In [15]:
arr_2d = np.array(([5,10,15],[20,25,30],[35,40,45]))

#Show
arr_2d
Out[15]:
array([[ 5, 10, 15],
       [20, 25, 30],
       [35, 40, 45]])
In [16]:
#Indexing row
arr_2d[1]
Out[16]:
array([20, 25, 30])
In [17]:
# Format is arr_2d[row][col] or arr_2d[row,col]

# Getting individual element value
arr_2d[1][0]
Out[17]:
20
In [17]:
# Getting individual element value
arr_2d[1,0]
Out[17]:
20
In [18]:
# 2D array slicing

#Shape (2,2) from top right corner
arr_2d[:2,1:]
Out[18]:
array([[10, 15],
       [25, 30]])
In [19]:
#Shape bottom row
arr_2d[2]
Out[19]:
array([35, 40, 45])
In [20]:
#Shape bottom row
arr_2d[2,:]
Out[20]:
array([35, 40, 45])

Fancy Indexing

Fancy indexing allows you to select entire rows or columns out of order,to show this, let's quickly build out a numpy array:

In [20]:
#Set up matrix
arr2d = np.zeros((10,10))
In [21]:
#Length of array
arr_length = arr2d.shape[1]
arr_length
Out[21]:
10
In [22]:
#Set up array

for i in range(arr_length):
    arr2d[i] = i
    
arr2d
Out[22]:
array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
       [1., 1., 1., 1., 1., 1., 1., 1., 1., 1.],
       [2., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [3., 3., 3., 3., 3., 3., 3., 3., 3., 3.],
       [4., 4., 4., 4., 4., 4., 4., 4., 4., 4.],
       [5., 5., 5., 5., 5., 5., 5., 5., 5., 5.],
       [6., 6., 6., 6., 6., 6., 6., 6., 6., 6.],
       [7., 7., 7., 7., 7., 7., 7., 7., 7., 7.],
       [8., 8., 8., 8., 8., 8., 8., 8., 8., 8.],
       [9., 9., 9., 9., 9., 9., 9., 9., 9., 9.]])

Fancy indexing allows the following

In [23]:
arr2d[[2,4,6,8]]
Out[23]:
array([[2., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [4., 4., 4., 4., 4., 4., 4., 4., 4., 4.],
       [6., 6., 6., 6., 6., 6., 6., 6., 6., 6.],
       [8., 8., 8., 8., 8., 8., 8., 8., 8., 8.]])
In [24]:
#Allows in any order
arr2d[[6,4,2,7]]
Out[24]:
array([[6., 6., 6., 6., 6., 6., 6., 6., 6., 6.],
       [4., 4., 4., 4., 4., 4., 4., 4., 4., 4.],
       [2., 2., 2., 2., 2., 2., 2., 2., 2., 2.],
       [7., 7., 7., 7., 7., 7., 7., 7., 7., 7.]])

More Indexing Help

Indexing a 2d matrix can be a bit confusing at first, especially when you start to add in step size.

Selection

Let's briefly go over how to use brackets for selection based off of comparison operators.

In [25]:
arr = np.arange(1,11)
arr
Out[25]:
array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])
In [26]:
arr > 4
Out[26]:
array([False, False, False, False,  True,  True,  True,  True,  True,
        True])
In [31]:
bool_arr = arr>4
In [32]:
bool_arr
Out[32]:
array([False, False, False, False,  True,  True,  True,  True,  True,  True], dtype=bool)
In [33]:
arr[bool_arr]
Out[33]:
array([ 5,  6,  7,  8,  9, 10])
In [34]:
arr[arr>2]
Out[34]:
array([ 3,  4,  5,  6,  7,  8,  9, 10])
In [37]:
x = 2
arr[arr>x]
Out[37]:
array([ 3,  4,  5,  6,  7,  8,  9, 10])
In [ ]:

See you on next concept......