CSR format (Compressed Sparse Row) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of CSR matrix multiplication

What is the output of the following code that multiplies two CSR matrices?

SciPy

import numpy as np
from scipy.sparse import csr_matrix

A = csr_matrix([[0, 0, 1], [1, 0, 0], [0, 2, 0]])
B = csr_matrix([[1, 0, 0], [0, 3, 0], [4, 0, 0]])

C = A.dot(B).toarray()
print(C)

A

[[0 3 0]
 [1 0 0]
 [0 0 0]]

B

[[0 0 0]
 [0 6 0]
 [4 0 0]]

C

[[4 0 0]
 [0 0 0]
 [0 6 0]]

D

[[4 0 0]
 [1 0 0]
 [0 6 0]]

💡 Hint

Remember that CSR matrix multiplication follows normal matrix multiplication rules.

Matrix A has non-zero elements at positions (0,2), (1,0), and (2,1). Matrix B has non-zero elements at (0,0), (1,1), and (2,0). Multiplying A and B, the element at (0,0) is A(0,2)*B(2,0) = 1*4=4, at (1,0) is A(1,0)*B(0,0)=1*1=1, and at (2,1) is A(2,1)*B(1,1)=2*3=6. All other elements are zero.

❓ data_output

intermediate

Number of non-zero elements in CSR matrix

Given the CSR matrix below, how many non-zero elements does it contain?

SciPy

from scipy.sparse import csr_matrix

matrix = csr_matrix([[0, 5, 0], [0, 0, 0], [7, 0, 8]])
print(matrix.nnz)

A 3

B 2

C 4

D 5

💡 Hint

Count all the non-zero values in the matrix.

The matrix has three non-zero values: 5 at (0,1), 7 at (2,0), and 8 at (2,2). So nnz (number of non-zero elements) is 3.

🔧 Debug

advanced

Identify the error in CSR matrix creation

What error will this code raise when trying to create a CSR matrix?

SciPy

from scipy.sparse import csr_matrix

# Data and indices lengths mismatch
data = [1, 2, 3]
indices = [0, 2]
indptr = [0, 2, 3]

csr = csr_matrix((data, indices, indptr), shape=(2, 3))

A No error, matrix created successfully

B ValueError: indices and data array must be the same length

C TypeError: unsupported operand type(s)

D IndexError: index out of bounds

💡 Hint

Check if the lengths of data and indices match.

The CSR format requires that the data and indices arrays have the same length because each data value corresponds to an index. Here, data has length 3 but indices has length 2, causing a ValueError.

🧠 Conceptual

advanced

Understanding CSR matrix components

Which of the following correctly describes the role of the 'indptr' array in a CSR matrix?

A 'indptr' stores the cumulative count of non-zero elements per row, marking start and end positions in 'data' and 'indices' arrays for each row.

B 'indptr' contains the column indices of non-zero elements.

C 'indptr' holds the actual non-zero data values of the matrix.

D 'indptr' is used to store the shape of the matrix.

💡 Hint

Think about how CSR stores rows efficiently.

'indptr' is an array of length (number_of_rows + 1). Each element points to the index in 'data' and 'indices' arrays where a row starts and ends. This allows quick access to each row's non-zero elements.

🚀 Application

expert

Efficient row slicing in CSR matrix

You want to extract the second row from a large CSR matrix efficiently. Which code snippet correctly extracts the second row as a CSR matrix?

SciPy

from scipy.sparse import csr_matrix

matrix = csr_matrix([[0, 1, 0], [2, 0, 3], [0, 0, 4]])

A

row = matrix[1, :]
print(type(row))

B

row = matrix[1]
print(type(row))

C

row = matrix.getrow(1)
print(type(row))

D

row = matrix.toarray()[1]
print(type(row))

💡 Hint

Look for a method designed for efficient row extraction in CSR.

matrix.getrow(1) returns the second row as a CSR matrix efficiently without converting the whole matrix to dense. matrix[1, :] returns a 1xN sparse matrix but can be less efficient. matrix[1] returns a 1D sparse matrix (not CSR). matrix.toarray()[1] converts entire matrix to dense, which is inefficient for large sparse matrices.

Practice

1. What is the main advantage of using the CSR format for storing matrices in data science?

easy

A. It stores all elements including zeros for faster access.

B. It saves memory by storing only non-zero elements and their positions.

C. It converts matrices into a list of lists format.

D. It automatically normalizes the matrix values.

Solution

1. Step 1: Understand CSR format purpose

   CSR format is designed to save space by storing only non-zero values and their positions in the matrix.

2. Step 2: Compare options with CSR features

   It saves memory by storing only non-zero elements and their positions. correctly describes this space-saving feature. Other options describe unrelated or incorrect features.

3. Final Answer:

   It saves memory by storing only non-zero elements and their positions. -> Option B

4. Quick Check:

   CSR = stores non-zero only [OK]

Hint: Remember CSR stores only non-zero values and their indices [OK]

Common Mistakes:

• Thinking CSR stores all elements including zeros
• Confusing CSR with dense matrix formats
• Assuming CSR normalizes data automatically

2. Which of the following is the correct way to create a CSR matrix from a dense NumPy array arr using SciPy?

easy

A. csr_matrix.to_csr(arr)

B. csr(arr)

C. sparse.csr(arr)

D. csr_matrix(arr)

Solution

1. Step 1: Recall SciPy CSR matrix creation syntax

   The correct function to create a CSR matrix from a dense array is csr_matrix() from scipy.sparse.

2. Step 2: Check each option

   csr_matrix(arr) uses the correct function name and syntax. Options B, C, and D are incorrect or invalid function calls.

3. Final Answer:

   csr_matrix(arr) -> Option D

4. Quick Check:

   Use csr_matrix() to convert dense to CSR [OK]

Hint: Use csr_matrix() function from scipy.sparse [OK]

Common Mistakes:

• Using incorrect function names like csr() or sparse.csr()
• Trying to call to_csr() method which doesn't exist
• Confusing with other sparse formats like COO

3. Given the following code, what will be the output of print(csr.data)?

import numpy as np
from scipy.sparse import csr_matrix

arr = np.array([[0, 0, 1], [2, 0, 0], [0, 3, 0]])
csr = csr_matrix(arr)
print(csr.data)

medium

A. [1 2 3]

B. [0 0 1 2 0 0 0 3 0]

C. [1 2 0 3]

D. [1 2 3 0]

Solution

1. Step 1: Understand csr.data attribute

   The data attribute of a CSR matrix stores only the non-zero values in row-major order.

2. Step 2: Identify non-zero elements in arr

   The non-zero elements are 1 (row 0, col 2), 2 (row 1, col 0), and 3 (row 2, col 1). So csr.data will be [1, 2, 3].

3. Final Answer:

   [1 2 3] -> Option A

4. Quick Check:

   csr.data = non-zero values list [OK]

Hint: csr.data holds only non-zero values in order [OK]

Common Mistakes:

• Expecting csr.data to include zeros
• Confusing csr.data with the full dense array
• Misordering the non-zero elements

4. Identify the error in the following code snippet that attempts to create a CSR matrix:

from scipy.sparse import csr_matrix

arr = [[0, 1], [2, 0]]
csr = csr_matrix(arr, shape=(2, 1))
print(csr.shape)

medium

A. The shape parameter is incompatible with the input array size.

B. The input array must be a NumPy array, not a list.

C. csr_matrix does not accept the shape parameter.

D. The print statement syntax is incorrect.

Solution

1. Step 1: Check input array and shape parameter

   The input array has shape (2, 2), but the shape parameter is set to (2, 1), which conflicts.

2. Step 2: Understand csr_matrix shape rules

   The shape parameter must match or be compatible with the input data shape. Here, (2, 1) is incompatible with (2, 2) input.

3. Final Answer:

   The shape parameter is incompatible with the input array size. -> Option A

4. Quick Check:

   Shape must match input array size [OK]

Hint: Ensure shape matches input array dimensions [OK]

Common Mistakes:

• Assuming lists cannot be input to csr_matrix
• Thinking csr_matrix disallows shape parameter
• Misreading print statement as error

5. You have a large sparse matrix representing user-item ratings with many zeros. You want to efficiently compute the sum of all ratings for each user (row). Which approach using CSR format is best?

hard

A. Use the CSR matrix's sum(axis=0) method to sum rows.

B. Convert the CSR matrix back to a dense array and use NumPy sum along axis 1.

C. Use the CSR matrix's sum(axis=1) method to sum non-zero values per row efficiently.

D. Manually iterate over all elements including zeros to sum each row.

Solution

1. Step 1: Understand CSR matrix row sum

   CSR format stores data row-wise, so summing along axis 1 is efficient and skips zeros.

2. Step 2: Evaluate options for efficiency

   Use the CSR matrix's sum(axis=1) method to sum non-zero values per row efficiently. uses sum(axis=1) directly on CSR, which is fast and memory efficient. Convert the CSR matrix back to a dense array and use NumPy sum along axis 1. wastes memory converting to dense. Manually iterate over all elements including zeros to sum each row. is slow. Use the CSR matrix's sum(axis=0) method to sum rows. sums columns, not rows.

3. Final Answer:

   Use the CSR matrix's sum(axis=1) method to sum non-zero values per row efficiently. -> Option C

4. Quick Check:

   Sum rows with csr.sum(axis=1) [OK]

Hint: Sum rows with csr.sum(axis=1) for efficiency [OK]

Common Mistakes:

• Converting to dense wastes memory
• Summing axis=0 sums columns, not rows
• Iterating manually is slow and unnecessary