Element-wise arithmetic in NumPy - Mini Project: Build & Apply

Element-wise arithmetic with NumPy arrays

📖 Scenario: Imagine you have two lists of daily temperatures from two different cities. You want to compare them by doing element-wise arithmetic operations like addition, subtraction, multiplication, and division.

🎯 Goal: You will create two NumPy arrays with exact temperature values, set a scaling factor, perform element-wise arithmetic operations between the arrays and the scaling factor, and finally print the results.

📋 What You'll Learn

Use NumPy arrays for the temperature data

Create a scaling factor variable

Perform element-wise addition, subtraction, multiplication, and division

Print the resulting arrays

💡 Why This Matters

🌍 Real World

Element-wise arithmetic is useful when comparing or combining data from different sources, like temperatures from multiple cities or sales data from different stores.

💼 Career

Data scientists often use element-wise operations to preprocess data, create new features, or analyze relationships between datasets efficiently.

1

Create two NumPy arrays with temperature data

Import NumPy as np. Create a NumPy array called city1_temps with these exact values: [20, 22, 19, 24, 21]. Create another NumPy array called city2_temps with these exact values: [18, 21, 20, 23, 22].

NumPy

import numpy as np
# Create city1_temps array with [20, 22, 19, 24, 21]
# Create city2_temps array with [18, 21, 20, 23, 22]

Hint

Use np.array([...]) to create NumPy arrays with the exact values given.

2

Set a scaling factor

Create a variable called scale and set it to the exact value 2.

NumPy

import numpy as np
city1_temps = np.array([20, 22, 19, 24, 21])
city2_temps = np.array([18, 21, 20, 23, 22])
# Create scale variable and set it to 2

Hint

Just assign the number 2 to a variable named scale.

3

Perform element-wise arithmetic operations

Create four new variables: added, subtracted, multiplied, and divided. Set added to the element-wise sum of city1_temps and city2_temps. Set subtracted to the element-wise difference of city1_temps minus city2_temps. Set multiplied to the element-wise product of city1_temps and scale. Set divided to the element-wise division of city2_temps by scale.

NumPy

import numpy as np
city1_temps = np.array([20, 22, 19, 24, 21])
city2_temps = np.array([18, 21, 20, 23, 22])
scale = 2
# Create added, subtracted, multiplied, divided with element-wise operations

Hint

Use +, -, *, and / operators between arrays and variables for element-wise operations.

4

Print the results

Print the variables added, subtracted, multiplied, and divided each on a separate line.

NumPy

import numpy as np
city1_temps = np.array([20, 22, 19, 24, 21])
city2_temps = np.array([18, 21, 20, 23, 22])
scale = 2
added = city1_temps + city2_temps
subtracted = city1_temps - city2_temps
multiplied = city1_temps * scale
divided = city2_temps / scale
# Print added, subtracted, multiplied, divided each on its own line

Hint

Use four print() statements, one for each variable.

Practice

1. What does element-wise arithmetic mean in numpy?

easy

A. Adding arrays only if they have the same number of elements

B. Applying operations to each pair of elements in arrays individually

C. Multiplying the sum of all elements in two arrays

D. Combining arrays into a single list

Solution

1. Step 1: Understand element-wise operation

   Element-wise arithmetic means applying the operation to each corresponding element in two arrays.

2. Step 2: Compare options

   Only Applying operations to each pair of elements in arrays individually correctly describes this as applying operations to each pair of elements individually.

3. Final Answer:

   Applying operations to each pair of elements in arrays individually -> Option B

4. Quick Check:

   Element-wise = operation on each element pair [OK]

Hint: Think: operation applies to each element pair separately [OK]

Common Mistakes:

• Confusing element-wise with whole-array operations
• Thinking arrays must be identical length only
• Assuming element-wise means concatenation

2. Which of the following is the correct syntax to add two numpy arrays a and b element-wise?

easy

A. np.sum(a, b)

B. a.add(b)

C. a + b

D. a.append(b)

Solution

1. Step 1: Check numpy addition methods

   The + operator performs element-wise addition in numpy.

2. Step 2: Evaluate options

   a.add(b) is invalid because numpy arrays do not have an add method. np.sum(a, b) computes sums, not element-wise addition. a.append(b) is a list method and errors on arrays.

3. Final Answer:

   a + b -> Option C

4. Quick Check:

   + operator adds arrays element-wise [OK]

Hint: Use + for element-wise addition [OK]

Common Mistakes:

• Using methods that don't exist on numpy arrays
• Trying to add arrays with Python list methods
• Confusing element-wise addition with matrix multiplication

3. What is the output of this code?

import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
print(x * y)

medium

A. [4 10 18]

B. [5 7 9]

C. [1 2 3 4 5 6]

D. Error: arrays must be same shape

Solution

1. Step 1: Understand element-wise multiplication

   Multiplying two numpy arrays multiplies each element pair: 1*4=4, 2*5=10, 3*6=18.

2. Step 2: Calculate output array

   The result is an array: [4, 10, 18].

3. Final Answer:

   [4 10 18] -> Option A

4. Quick Check:

   Element-wise multiply: [1*4, 2*5, 3*6] = [4 10 18] [OK]

Hint: Multiply arrays element-wise: multiply each pair [OK]

Common Mistakes:

• Adding instead of multiplying elements
• Expecting concatenation of arrays
• Thinking multiplication sums elements

4. Identify the error in this code snippet:

import numpy as np
x = np.array([1, 2, 3])
y = np.array([4, 5])
print(x + y)

medium

A. No error, output is [5 7 3]

B. Syntax error in print statement

C. Missing import statement for numpy

D. Arrays have incompatible shapes for element-wise addition

Solution

1. Step 1: Check array shapes

   Array x has shape (3,), y has shape (2,). They are not compatible for element-wise addition.

2. Step 2: Understand numpy broadcasting rules

   Broadcasting requires shapes to be compatible; here they differ and cause an error.

3. Final Answer:

   Arrays have incompatible shapes for element-wise addition -> Option D

4. Quick Check:

   Shape mismatch causes error in element-wise addition [OK]

Hint: Check array shapes before element-wise operations [OK]

Common Mistakes:

• Assuming arrays auto-align despite different lengths
• Ignoring broadcasting rules
• Thinking Python lists behave like numpy arrays

5. Given two arrays:

a = np.array([[1, 2], [3, 4]])
b = np.array([10, 20])

What is the result of a + b and why?

hard

A. [[11 22]
[13 24]] because b is broadcasted to each row of a

B. [[10 20]
[10 20]] because b replaces a

C. [[1 2]
[3 4]] because addition is not possible

D. Error due to shape mismatch

Solution

1. Step 1: Analyze shapes of arrays

   a is shape (2,2), b is shape (2,). Numpy broadcasts b across rows of a.

2. Step 2: Perform element-wise addition with broadcasting

   Add b to each row of a: first row [1+10, 2+20], second row [3+10, 4+20].

3. Final Answer:

   [[11 22] [13 24]] -> Option A

4. Quick Check:

   Broadcasting adds b to each row of a [OK]

Hint: Broadcast smaller array to match larger shape for element-wise ops [OK]

Common Mistakes:

• Expecting error due to different shapes
• Thinking b replaces a instead of broadcasting
• Ignoring numpy broadcasting rules