NumPy arrays through indexing and slicing.

Tuesday 2 April 2024

NumPy arrays through indexing and slicing.

Ways to access and manipulate elements within NumPy arrays through indexing and slicing.

Fundamentals

Zero-Based Indexing: Like Python lists, NumPy array indexing starts from 0. The first element is at index 0, the second at index 1, and so on.
Multidimensional Arrays: Indexing becomes more interesting with multiple dimensions (matrices, tensors).

Accessing Elements

Single Element:

For a 1D Array: array_name[index]
Python
arr = np.array([5, 10, -2, 6])
first_element = arr[0] # Accesses the value 5
For a 2D array (matrix): array_name[row_index, column_index]
Python
matrix = np.array([[1, 2, 3], [4, 5, 6]])
element_at_0_1 = matrix[0, 1] # Accesses the value 2 (zero-based)

Slicing

Slicing extracts sub-arrays using the following syntax: array_name[start:end:step]

start: Index of the first element to include (inclusive)
end: Index where the slice ends (exclusive)
step: The step size between elements to include

Examples:

Python

import numpy as np

arr = np.arange(12)
print(arr) # [ 0 1 2 3 4 5 6 7 8 9 10 11]

# Get elements from index 2 to 6 (exclusive)
sub_arr = arr[2:6] # [ 2 3 4 5]

# Every other element
every_other = arr[::2] # [ 0 2 4 6 8 10]

# Reverse the array
reversed_arr = arr[::-1] # [11 10 9 8 7 6 5 4 3 2 1 0]

Slicing Multidimensional Arrays

Each dimension: Separate slice operations with commas.
Colon for all elements: A colon in a dimension means "take all elements along that dimension.

Python

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

# First row
first_row = matrix[0, :]

# Second column
second_col = matrix[:, 1]

# Top-left 2x2 sub-matrix
top_left_corner = matrix[:2, :2]

Important Notes:

Modifying Slices: Modifying a slice obtained from NumPy arrays also modifies the original array. This happens because slices are often views into the original data.
Copy if Needed: If you want to work with a separate copy, explicitly make a copy of the slice using .copy().

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Assignments to practice NumPy indexing and slicing, along with solutions.

Assignment 1: Basic Slicing

Instructions: Given the following array,
Python
import numpy as np
data = np.arange(1, 21).reshape(4, 5)

Extract the elements in the second row.
Extract the elements from the second column to the end.
Create a sub-array containing the bottom-right 2x2 corner.
Select every other element from the first and third rows.

Solution:
Python
# Second row
second_row = data[1, :]

# Second column to end
second_col_onwards = data[:, 1:]

# Bottom-right corner
bottom_right = data[2:, 3:]

# Every other element, first and third rows
select_elements = data[[0, 2], ::2]

Assignment 2: Calculation with Slices

Instructions: Consider the following array:
Python
temperatures = np.array([16, 25, -2, 19, 21])

Calculate the average of the positive temperatures.
Select temperatures below the freezing point of water (0 degrees Celsius) and replace them with 0.

Solution:
Python
# Average of positive temperatures
positive_temps = temperatures[temperatures > 0]
average_positive = np.mean(positive_temps)

# Handling subzero temperatures
temperatures[temperatures < 0] = 0

Assignment 3: Matrix Manipulation

Instructions: Given a matrix:
Python
matrix = np.array([[10, 5, -1],
[3, 8, 2],
[6, -4, 9]])

Reverse the order of the columns.
Swap the first and last rows.
Extract the values in the diagonal (top-left to bottom-right).

Solution
Python
# Reverse columns
reversed_cols = matrix[:, ::-1]

# Swap rows
matrix[[0, 2], :] = matrix[[2, 0], :]

# Extract diagonal elements
diagonal_elements = matrix.diagonal()

Tips

Experiment: Try different variations of slicing to solidify your understanding.
Visualization: For matrices, print arrays before and after manipulation to visually confirm your results.

Enhancements