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 [14]:

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

#Show
arr_2d









    Out[14]:





array([[ 5, 10, 15],
       [20, 25, 30],
       [35, 40, 45]])



In [15]:

    
#Indexing row
arr_2d[1]









    Out[15]:





array([20, 25, 30])



In [16]:

    
# Format is arr_2d[row][col] or arr_2d[row,col]

# Getting individual element value
arr_2d[1][0]









    Out[16]:





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 [21]:

    
#Set up matrix
arr2d = np.zeros((10,10))



In [22]:

    
#Length of array
arr_length = arr2d.shape[1]



In [23]:

    
#Set up array

for i in range(arr_length):
    arr2d[i] = i
    
arr2d









    Out[23]:





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 [24]:

    
arr2d[[2,4,6,8]]









    Out[24]:





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 [25]:

    
#Allows in any order
arr2d[[6,4,2,7]]









    Out[25]:





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. Try google image searching NumPy indexing to fins useful images, like this one:

Selection

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



In [28]:

    
arr = np.arange(1,11)
arr









    Out[28]:





array([ 1,  2,  3,  4,  5,  6,  7,  8,  9, 10])



In [30]:

    
arr > 4









    Out[30]:





array([False, False, False, False,  True,  True,  True,  True,  True,  True], dtype=bool)



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])