`numpy` Exercises

These exercises test your understanding of the NumPy concepts covered in the introduction notebook.

Exercise 1: Import and Basic Array Creation

Task: Import NumPy with the standard import command and create a NumPy array from the list [2, 4, 6, 8, 10, 12]. Print the array, its data type, and its shape.

Exercise 2: Array Indexing and Slicing

Task: Using the array you created in Exercise 1:

Print the first element
Print the last element
Print elements from index 2 to 4 (inclusive of 2, exclusive of 5)
Print every second element

Exercise 3: Element-wise Operations

Task: Create a NumPy array arr = np.array([1, 4, 9, 16, 25]). Perform the following operations and print the results:

Multiply each element by 3
Add 10 to each element
Calculate the square root of each element
Apply the sine function to each element

Exercise 4: Array Operations with Two Arrays

Task: Create two NumPy arrays:

arr1 = np.array([1, 2, 3, 4, 5])
arr2 = np.array([10, 20, 30, 40, 50])

Perform element-wise operations and print the results:

Add the two arrays
Subtract arr1 from arr2
Multiply the two arrays
Divide arr2 by arr1

Exercise 5: Shape Mismatch Error

Task: Create two arrays with different lengths:

arr_a = np.array([1, 2, 3, 4])
arr_b = np.array([10, 20])

Try to add these arrays together. What happens? Write the code and explain the error in a comment.

Exercise 6: Reductive Operations

Task: Create a NumPy array data = np.array([12, 8, 15, 3, 7, 20, 11, 9]). Calculate and print:

The sum of all elements
The mean (average) of all elements
The maximum value
The minimum value
The standard deviation

Exercise 7: Array Manipulation

Task: Create a NumPy array numbers = np.array([5, 2, 8, 1, 9, 3]). Perform the following operations:

Sort the array and print the result
Calculate the cumulative sum and print the result
Create a new array with duplicates: with_duplicates = np.array([5, 2, 8, 1, 9, 3, 5, 2, 1]) and find the unique elements

Exercise 8: List vs NumPy Comparison

Task: Compare the flexibility of lists vs NumPy arrays:

Create a Python list containing mixed data types: mixed_list = [1, 'hello', 3.14, True]
Try to create a NumPy array from this list. What happens to the data types?
Create a list of numbers: num_list = [1, 2, 3, 4, 5]
Try to multiply the entire list by 2 using num_list * 2. What happens?
Create a NumPy array from the same numbers and multiply by 2. Compare the results.

Exercise 9: Performance Comparison

Task: Compare the performance of list comprehension vs NumPy operations:

Import the time module
Create a range of 50,000 numbers using numpy np.arange()
Time how long it takes to square each number using a list comprehension, i.e. the syntax [x**2 for x in myarray]
Time how long it takes to square each number using NumPy operations
Calculate and print how many times faster the NumPy operation is

Exercise 10: Complex Operations

Task: Create a NumPy array representing angles in degrees: angles_deg = np.array([0, 30, 45, 60, 90, 120, 180]) 1. Convert these angles to radians (hint: multiply by π/180, use np.pi) 2. Calculate the sine and cosine of each angle 3. Verify that sin²(x) + cos²(x) = 1 for each angle (use np.sin() and np.cos()) 4. Print all results

Challenge 1: Temperature Conversion

Task: You have temperature readings in Celsius: celsius_temps = np.array([0, 10, 20, 25, 30, 35, 40])

Convert all temperatures to Fahrenheit using the formula: F = (C × 9/5) + 32
Convert all temperatures to Kelvin using the formula: K = C + 273.15
Calculate the temperature range (max - min) for each scale

Challenge 2: Kinetic energy

Task Given arrays of mass (kg) and velocity (m/s) for several objects:

# copy and paste this code below
masses = np.array([2.0, 1.5, 3.0, 0.5])      # in kilograms
velocities = np.array([10.0, 20.0, 15.0, 5.0]) # in meters per second

Calculate the kinetic energy $K$ for each object using the formula:

\[K = \dfrac{1}{2}m v^2\]

Calculate the total kinetic energy of the system (sum of all objects)

Challenge 3: Temperature Analysis

Task: Given a NumPy array of daily temperatures for 30 days:

temperatures = np.array([23.5, 24.0, 21.2, 25.6, 22.8, 23.9, 26.1, 27.3, 21.7, 22.5,
                         24.6, 25.8, 20.9, 22.3, 24.7, 26.0, 27.5, 21.0, 22.9, 24.8,
                         25.9, 27.6, 20.8, 22.7, 24.5, 26.2, 27.7, 20.5, 22.6, 24.9])

Perform the following tasks:

Find the top 3 hottest days and their temperatures.
Calculate the day-to-day percentage change in temperature.

--- title: '`numpy` Exercises' jupyter: python3 --- These exercises test your understanding of the NumPy concepts covered in the introduction notebook. ## Exercise 1: Import and Basic Array Creation **Task:** Import NumPy with the standard `import` command and create a NumPy array from the list `[2, 4, 6, 8, 10, 12]`. Print the array, its data type, and its shape. ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 2: Array Indexing and Slicing **Task:** Using the array you created in Exercise 1: - Print the first element - Print the last element - Print elements from index 2 to 4 (inclusive of 2, exclusive of 5) - Print every second element ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 3: Element-wise Operations **Task:** Create a NumPy array `arr = np.array([1, 4, 9, 16, 25])`. Perform the following operations and print the results: - Multiply each element by 3 - Add 10 to each element - Calculate the square root of each element - Apply the sine function to each element ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 4: Array Operations with Two Arrays **Task:** Create two NumPy arrays: - `arr1 = np.array([1, 2, 3, 4, 5])` - `arr2 = np.array([10, 20, 30, 40, 50])` Perform element-wise operations and print the results: - Add the two arrays - Subtract arr1 from arr2 - Multiply the two arrays - Divide arr2 by arr1 ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 5: Shape Mismatch Error **Task:** Create two arrays with different lengths: - `arr_a = np.array([1, 2, 3, 4])` - `arr_b = np.array([10, 20])` Try to add these arrays together. What happens? Write the code and explain the error in a comment. ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 6: Reductive Operations **Task:** Create a NumPy array `data = np.array([12, 8, 15, 3, 7, 20, 11, 9])`. Calculate and print: - The sum of all elements - The mean (average) of all elements - The maximum value - The minimum value - The standard deviation ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 7: Array Manipulation **Task:** Create a NumPy array `numbers = np.array([5, 2, 8, 1, 9, 3])`. Perform the following operations: - Sort the array and print the result - Calculate the cumulative sum and print the result - Create a new array with duplicates: `with_duplicates = np.array([5, 2, 8, 1, 9, 3, 5, 2, 1])` and find the unique elements ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 8: List vs NumPy Comparison **Task:** Compare the flexibility of lists vs NumPy arrays: 1. Create a Python list containing mixed data types: `mixed_list = [1, 'hello', 3.14, True]` 2. Try to create a NumPy array from this list. What happens to the data types? 3. Create a list of numbers: `num_list = [1, 2, 3, 4, 5]` 4. Try to multiply the entire list by 2 using `num_list * 2`. What happens? 5. Create a NumPy array from the same numbers and multiply by 2. Compare the results. ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 9: Performance Comparison **Task:** Compare the performance of list comprehension vs NumPy operations: 1. Import the `time` module 2. Create a range of 50,000 numbers using numpy `np.arange()` 3. Time how long it takes to square each number using a **list comprehension**, i.e. the syntax `[x**2 for x in myarray]` 4. Time how long it takes to square each number using NumPy operations 5. Calculate and print how many times faster the NumPy operation is ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Exercise 10: Complex Operations **Task:** Create a NumPy array representing angles in degrees: `angles_deg = np.array([0, 30, 45, 60, 90, 120, 180])` 1. Convert these angles to radians (hint: multiply by π/180, use `np.pi`) 2. Calculate the sine and cosine of each angle 3. Verify that sin²(x) + cos²(x) = 1 for each angle (use `np.sin()` and `np.cos()`) 4. Print all results ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Challenge 1: Temperature Conversion **Task:** You have temperature readings in Celsius: `celsius_temps = np.array([0, 10, 20, 25, 30, 35, 40])` 1. Convert all temperatures to Fahrenheit using the formula: F = (C × 9/5) + 32 2. Convert all temperatures to Kelvin using the formula: K = C + 273.15 3. Calculate the temperature range (max - min) for each scale ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Challenge 2: Kinetic energy **Task** Given arrays of mass (kg) and velocity (m/s) for several objects: ```python # copy and paste this code below masses = np.array([2.0, 1.5, 3.0, 0.5]) # in kilograms velocities = np.array([10.0, 20.0, 15.0, 5.0]) # in meters per second ``` 1. Calculate the kinetic energy $K$ for each object using the formula: $$K = \dfrac{1}{2}m v^2$$ 2. Calculate the total kinetic energy of the system (sum of all objects) ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ``` ## Challenge 3: Temperature Analysis **Task:** Given a NumPy array of daily temperatures for 30 days: ```python temperatures = np.array([23.5, 24.0, 21.2, 25.6, 22.8, 23.9, 26.1, 27.3, 21.7, 22.5, 24.6, 25.8, 20.9, 22.3, 24.7, 26.0, 27.5, 21.0, 22.9, 24.8, 25.9, 27.6, 20.8, 22.7, 24.5, 26.2, 27.7, 20.5, 22.6, 24.9]) ``` Perform the following tasks: 1. Find the top 3 hottest days and their temperatures. 2. Calculate the day-to-day percentage change in temperature. ```{pyodide} #| caption: "▶ Ctrl/Cmd+Enter | ⇥ Ctrl/Cmd+] | ⇤ Ctrl/Cmd+[" # Your code here ```