NumPy - Advanced Indexing

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Advanced indexing offers a robust method to select specific elements from a NumPy array based on predetermined conditions or guidelines.

While basic indexing, like array[1:4] gives you a "view" of the original array (where modifications to the slice affect the original data), advanced indexing always creates a copy of the selected data.

It allows you to select elements from an ndarray that is a non-tuple sequence, ndarray object of integer or Boolean data type, or a tuple with at least one item being a sequence object. This method is helpful in dynamic data selection as well as conditional data extraction.

There are two types of advanced indexing −

• Integer Indexing
• Boolean Array Indexing

Integer Indexing

This allows you to select specific elements from an array using their exact positions (indices) based on its N dimensional index. Each integer array represents the number of indexes into that dimension.

If the number of integer arrays corresponds to the dimensions of the target ndarray, selecting items becomes simple and straightforward. It's like selecting item at x, y, z position.

Example: Selecting Elements by Indices

The following example selects one element from each row of the array using integer arrays for both rows and columns. The selection includes elements at (0,0), (1,1) and (2,0) from the first array. Following is the code −

import numpy as np 
x = np.array([[1, 2], [3, 4], [5, 6]]) 
y = x[[0,1,2], [0,1,0]] 
print(x)
print('The new array is :\n', y)

Following is the output of the above code −

[[1 2]
 [3 4]
 [5 6]]
The new array is :
 [1 4 5]

Example: Selecting Corner Elements

In the following example, elements placed at corners of a 4X3 array are selected. The row indices of selection are [0, 0] and [3,3] whereas the column indices are [0,2] and [0,2].

import numpy as np
x = np.array([[ 0,  1,  2],[ 3,  4,  5],[ 6,  7,  8],[ 9, 10, 11]]) 
print('Our array is: \n', x)
rows = np.array([[0,0],[3,3]])
cols = np.array([[0,2],[0,2]]) 
y = x[rows,cols] 
print('The corner elements of this array are: \n', y)

Following is the output of the above code −

Our array is: 
 [[ 0  1  2]
 [ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]]
The corner elements of this array are: 
 [[ 0  2]
 [ 9 11]]

Example: Accessing Specific Marks

In this example we have 2D array which contains marks of three different students representing in rows and marks in three columns of different subjects Hindi, Maths, English.

Now, we will see how to access a score of student 1 in Hindi and score of student 2 in Maths. Following is the code −

import numpy as np
marks = np.array([[85, 99, 88], [78, 93, 85], [86, 45, 90]])
specific_results = marks[[0, 1], [0, 1]]
print('Marks:\n', marks)
print('Selected marks: \n', specific_results)

Output of the above code is as follows −

Marks:
 [[85 99 88]
 [78 93 85]
 [86 45 90]]
Selected marks: 
 [85 93]

Example: Index Out of Bounds Error

In NumPy an index error (index out of bounds) occurs when you try to access an element in the array using the index that is outside the valid range of array dimensions.

Let us understand this with example where an array contains 3 rows but the code attempts to access the 4th row (index 3), throws index error −

import numpy as np
x = np.array([[0, 1], [2, 3], [4, 65]])
print('The 2D arrays is : \n', x)
print(x[3,1])

Following is the output of the above code −

The 2D arrays is : 
 [[ 0  1]
 [ 2  3]
 [ 4 65]]
Traceback (most recent call last):
  File "/home/cg/root/22245/main.py", line 4, in 
    print(x[3,1])
IndexError: index 3 is out of bounds for axis 0 with size 3

Boolean Array Indexing

NumPy's Boolean indexing lets you select array elements that meet a certain condition. It involves creating a Boolean array where each element matches up with a True or False condition. The elements from the original array is selected where the Boolean array shows True.

This approach works well to filter data using logical conditions, like comparison operations. It is a powerful tool to pull out specific values from arrays.

Example: Using a Boolean Array to Select Specific Elements

This code illustrates how to use a Boolean array as a mask for selecting certain elements from a NumPy array. The Boolean array specifies which elements are to be included (True) or excluded (False) in the final array.

import numpy as np

arr = np.array([10, 20, 30, 40, 50])
bool_array = np.array([True, False, True, False, True])
selected_elements = arr[bool_array]

print("Original array:", arr)
print("Boolean array:", bool_array)
print("Selected elements:", selected_elements)

Output of the above code is as follows −

Original array: [10 20 30 40 50]
Boolean array: [ True False  True False  True]
Selected elements: [10 30 50]

Example: Filtering Items Greater Than 5

In this example, items greater than 5 are returned as a result of Boolean indexing.

import numpy as np 
x = np.array([[ 0,  1,  2],[ 3,  4,  5],[ 6,  7,  8],[ 9, 10, 11]]) 
print('Our array is: \n', x)  
print('The items greater than 5 are:' , x[x > 5])

When we run above program, it produces following result −

Our array is: 
 [[ 0  1  2]
 [ 3  4  5]
 [ 6  7  8]
 [ 9 10 11]]
The items greater than 5 are: [ 6  7  8  9 10 11]

Example: Removing NaN Values

In this example, NaN (Not a Number) elements are omitted by using ~ (complement operator).

import numpy as np 
a = np.array([np.nan, 1,2,np.nan,3,4,5]) 
print(a[~np.isnan(a)])

When we run above program, it produces following result −

[1. 2. 3. 4. 5.]

Example: Filtering Complex Numbers

The following example shows how to filter out the complex numbers from an array.

import numpy as np 
a = np.array([1, 2+6j, 5, 3.5+5j]) 
print(a[np.iscomplex(a)])

Output of the above code is as follows −

[2. +6.j 3.5+5.j]

Example: Extracting Even Numbers

Let us see how to extract even numbers from an array using boolean indexing −

import numpy as np
x = np.array([1, 2, 3, 4, 5, 6, 7, 8])
print('The even numbers are:', x[x % 2 == 0])

Following is the output of the above code −

The even numbers are: [2 4 6 8]