np.einsum() for efficient computation in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to compute the sum of elements in array using np.einsum.

NumPy

import numpy as np
arr = np.array([1, 2, 3, 4])
sum_val = np.einsum('[1]', arr)
print(sum_val)

Drag options to blanks, or click blank then click option'

A'i->'

B'i->i'

C'ij->i'

D'i,i->'

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'i,i->' which expects two arrays.

Using 'ij->i' which is for 2D arrays.

Using 'i->i' which returns the array unchanged.

The subscript 'i->' tells np.einsum to sum over the index 'i', resulting in the sum of all elements.

2fill in blank

medium

Complete the code to compute the dot product of two vectors using np.einsum.

NumPy

import numpy as np
v1 = np.array([1, 2, 3])
v2 = np.array([4, 5, 6])
dot_product = np.einsum('[1]', v1, v2)
print(dot_product)

Drag options to blanks, or click blank then click option'

A'ij,jk->ik'

B'i,j->ij'

C'i,i->'

D'i->'

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'i->' which sums only one vector.

Using 'ij,jk->ik' which is for matrix multiplication.

Using 'i,j->ij' which computes outer product.

The subscript 'i,i->' multiplies elements of v1 and v2 at the same index and sums the result, computing the dot product.

3fill in blank

hard

Fix the error in the code to perform matrix multiplication using np.einsum.

NumPy

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

Drag options to blanks, or click blank then click option'

A'ij,jk->ik'

B'ij,ik->jk'

C'ji,kj->ik'

D'ij,jk->ij'

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'ij,ik->jk' which mismatches indices.

Using 'ji,kj->ik' which reverses indices incorrectly.

Using 'ij,jk->ij' which does not reduce the summed index.

The subscript 'ij,jk->ik' correctly performs matrix multiplication by summing over the shared index 'j'.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps words to their lengths only if length is greater than 3.

NumPy

words = ['apple', 'bat', 'carrot', 'dog']
lengths = {word: [1] for word in words if [2]

Drag options to blanks, or click blank then click option'

Alen(word)

Blen(word) > 3

Cword

Dlen(words)

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'word' as value instead of length.

Using 'len(words)' which is the total number of words.

Using condition without comparison operator.

We use len(word) to get the length and filter words with length greater than 3.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their lengths only if length is greater than 3.

NumPy

words = ['apple', 'bat', 'carrot', 'dog']
lengths = [1]: [2] for word in words if [3]

Drag options to blanks, or click blank then click option'

Aword.upper()

Blen(word)

Clen(word) > 3

Dword.lower()

Attempts:

3 left

💡 Hint

Common Mistakes

Using word.lower() instead of upper().

Using word as key without conversion.

Missing the length condition or using wrong comparison.

The key is the uppercase word, the value is its length, and the condition filters words longer than 3 characters.

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