np.einsum() for efficient computation in NumPy - Mini Project: Build & Apply

Using np.einsum() for Efficient Computation

📖 Scenario: Imagine you work in a small company that analyzes sales data. You have two sets of numbers: the quantity of items sold and the price per item. You want to find the total sales amount for each item quickly and efficiently.

🎯 Goal: You will learn how to use np.einsum() to multiply arrays element-wise and sum over specific axes, which is a fast way to do calculations like total sales.

📋 What You'll Learn

Create two numpy arrays with exact values

Define a configuration variable for the operation

Use np.einsum() with the correct subscripts to compute total sales

Print the resulting array showing total sales per item

💡 Why This Matters

🌍 Real World

In real business scenarios, fast and memory-efficient calculations like total sales help companies make quick decisions.

💼 Career

Data scientists and analysts often use <code>np.einsum()</code> to speed up numerical computations in data processing and machine learning.

1

Create the sales quantity and price arrays

Create a numpy array called quantities with values [2, 3, 5] representing items sold. Also create a numpy array called prices with values [10, 20, 30] representing price per item.

NumPy

# Create the numpy arrays quantities and prices
# Your code here

Hint

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

2

Define the einsum operation string

Create a string variable called operation and set it to 'i,i->' which tells np.einsum() to multiply elements of two 1D arrays and sum the result.

NumPy

import numpy as np
quantities = np.array([2, 3, 5])
prices = np.array([10, 20, 30])
# Define the einsum operation string
# Your code here

Hint

The string 'i,i->' means multiply elements with index i from both arrays and sum all results.

3

Calculate total sales using np.einsum()

Use np.einsum() with the operation string and arrays quantities and prices to calculate the total sales amount. Store the result in a variable called total_sales.

NumPy

import numpy as np
quantities = np.array([2, 3, 5])
prices = np.array([10, 20, 30])
operation = 'i,i->'
# Calculate total_sales using np.einsum
# Your code here

Hint

Call np.einsum() with the operation string and the two arrays in order.

4

Print the total sales amount

Print the variable total_sales to display the total sales amount.

NumPy

import numpy as np
quantities = np.array([2, 3, 5])
prices = np.array([10, 20, 30])
operation = 'i,i->'
total_sales = np.einsum(operation, quantities, prices)
# Print total_sales
# Your code here

Hint

Use print(total_sales) to show the result.

Practice

1. What is the main purpose of np.einsum() in numpy?

easy

A. To perform efficient and readable array operations using Einstein summation notation

B. To create random arrays with specific distributions

C. To sort arrays in ascending order

D. To reshape arrays into different dimensions

Solution

1. Step 1: Understand the function's goal

   np.einsum() uses Einstein summation notation to express complex array operations clearly and efficiently.

2. Step 2: Compare with other options

   Options B, C, and D describe unrelated numpy functions like random generation, sorting, and reshaping.

3. Final Answer:

   To perform efficient and readable array operations using Einstein summation notation -> Option A

4. Quick Check:

   Purpose of np.einsum() = To perform efficient and readable array operations using Einstein summation notation [OK]

Hint: Remember: einsum is for smart, fast array math [OK]

Common Mistakes:

• Confusing einsum with random array creation
• Thinking einsum sorts or reshapes arrays
• Assuming einsum is only for dot products

2. Which of the following is the correct syntax to compute the matrix product of two 2D arrays A and B using np.einsum()?

easy

A. np.einsum('ij,jk->ik', A, B)

B. np.einsum('ik,jk->ij', A, B)

C. np.einsum('ij,ik->jk', A, B)

D. np.einsum('ji,kj->ik', A, B)

Solution

1. Step 1: Recall matrix multiplication indices

   Matrix multiplication of A (shape ixj) and B (shape jxk) results in shape ixk, summing over j.

2. Step 2: Match einsum subscripts

   np.einsum('ij,jk->ik', A, B) uses 'ij,jk->ik', which correctly sums over j and produces ixk output.

3. Final Answer:

   np.einsum('ij,jk->ik', A, B) -> Option A

4. Quick Check:

   Matrix product einsum = np.einsum('ij,jk->ik', A, B) [OK]

Hint: Use 'ij,jk->ik' for matrix multiplication [OK]

Common Mistakes:

• Mixing up indices order in the subscript string
• Using wrong output indices after ->
• Confusing which axis to sum over

3. Given the code:

import numpy as np
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
result = np.einsum('ij,ij->i', A, B)
print(result)

What is the output?

medium

A. [19 43]

B. [17 43]

C. [23 53]

D. [17 53]

Solution

1. Step 1: Understand the einsum subscripts 'ij,ij->i'

   This sums element-wise multiplication over the second index j, keeping the first index i.

2. Step 2: Calculate for each i

   For i=0: (1*5)+(2*6)=5+12=17; For i=1: (3*7)+(4*8)=21+32=53.

3. Final Answer:

   [17 53] -> Option D

4. Quick Check:

   Element-wise sum over j = [17 53] [OK]

Hint: Sum over repeated indices, keep others [OK]

Common Mistakes:

• Summing over wrong axis
• Confusing output indices in einsum
• Calculating element-wise product incorrectly

4. Identify the error in this code snippet:

import numpy as np
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
result = np.einsum('ij,jk->ik', A, B)
print(result)

and choose the correct fix.

medium

A. Ensure B has shape (2, 2) and use 'ij,jk->ik' as is

B. No error; code runs correctly

C. Swap arrays to np.einsum('jk,ij->ik', B, A)

D. Change subscript to 'ij,ik->jk' to match shapes

Solution

1. Step 1: Check array shapes and einsum subscripts

   A and B both have shape (2,2). The subscript 'ij,jk->ik' expects B's first dimension (j) to match A's second dimension (j), which it does.

2. Step 2: Verify if code runs

   Shapes match perfectly for matrix multiplication. No error; the code runs correctly.

3. Final Answer:

   No error; code runs correctly -> Option B

4. Quick Check:

   No error; code runs correctly [OK]

Hint: Check array shapes match einsum indices [OK]

Common Mistakes:

• Assuming code errors without checking shapes
• Changing subscripts incorrectly
• Swapping arrays unnecessarily

5. You have a 3D array data with shape (10, 5, 4) representing 10 samples, 5 features, and 4 time points. Using np.einsum(), how do you compute the sum of products of features and time points for each sample, resulting in a 1D array of length 10?

hard

A. np.einsum('ijk,ijk->k', data, data)

B. np.einsum('ijk,ijk->j', data, data)

C. np.einsum('ijk,ijk->i', data, data)

D. np.einsum('ijk,ijk->ij', data, data)

Solution

1. Step 1: Understand the dimensions and desired output

   Data shape is (samples=10, features=5, time=4). We want to sum over features and time, keeping samples dimension.

2. Step 2: Use einsum to sum over j and k, keep i

   Subscript 'ijk,ijk->i' multiplies element-wise and sums over j and k, resulting in length 10 array.

3. Final Answer:

   np.einsum('ijk,ijk->i', data, data) -> Option C

4. Quick Check:

   Sum over features and time = np.einsum('ijk,ijk->i', data, data) [OK]

Hint: Sum over repeated indices, keep sample index [OK]

Common Mistakes:

• Summing over wrong axes
• Confusing output indices in einsum
• Expecting 2D output instead of 1D