CSC format (Compressed Sparse Column) in SciPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of CSC matrix data arrays

Given the following code creating a CSC matrix, what is the output of the data, indices, and indptr arrays?

SciPy

from scipy.sparse import csc_matrix
import numpy as np

matrix = np.array([[0, 0, 1],
                   [2, 0, 0],
                   [0, 3, 4]])
csc = csc_matrix(matrix)
print(csc.data)
print(csc.indices)
print(csc.indptr)

A

[2 3 1 4]
[1 2 0 2]
[0 1 2 4]

B

[1 2 3 4]
[2 0 2 2]
[0 1 2 4]

C

[1 2 3 4]
[1 0 2 2]
[0 1 2 4]

D

[2 3 4 1]
[2 0 1 2]
[0 1 2 4]

💡 Hint

Remember CSC stores data column-wise. Check each column's non-zero elements.

The CSC format stores non-zero values column by column. The data array holds these values in order. The indices array holds the row indices of each data element. The indptr array points to column start positions in data.

For the given matrix:

[[0, 0, 1],
 [2, 0, 0],
 [0, 3, 4]]

Column 0 has non-zero value 2 at row 1.

Column 1 has non-zero value 3 at row 2.

Column 2 has non-zero values 1 at row 0 and 4 at row 2.

So data = [1, 2, 3, 4] is incorrect order; correct order is [2, 3, 1, 4] which matches option A.

❓ data_output

intermediate

Number of non-zero elements in CSC matrix

What is the number of non-zero elements in the following CSC matrix?

SciPy

from scipy.sparse import csc_matrix
import numpy as np

matrix = np.array([[0, 5, 0],
                   [0, 0, 0],
                   [7, 0, 9]])
csc = csc_matrix(matrix)
print(csc.nnz)

A 4

B 2

C 5

D 3

💡 Hint

Count all non-zero values in the matrix.

The matrix has three non-zero values: 5, 7, and 9.

So the number of non-zero elements (nnz) is 3.

🔧 Debug

advanced

Identify the error in CSC matrix creation

Which option will cause an error when creating a CSC matrix from the given data arrays?

SciPy

from scipy.sparse import csc_matrix
import numpy as np

data = np.array([1, 2, 3])
indices = np.array([0, 1, 2])
indptr = np.array([0, 1, 2, 3])

csc = csc_matrix((data, indices, indptr), shape=(3, 3))

A csc_matrix((data, indptr, indices), shape=(3, 3))

B csc_matrix((data, indices, indptr), shape=(3, 3))

C csc_matrix((data, indices), shape=(3, 3))

D csc_matrix((data, indices, indptr), shape=(3, 2))

💡 Hint

Check the order of the tuple arguments for CSC matrix constructor.

The CSC matrix constructor expects a tuple of (data, indices, indptr) in that order.

Option A swaps indptr and indices, causing a ValueError.

Option A misses indptr, causing a TypeError.

Option A has a shape mismatch causing a ValueError.

🚀 Application

advanced

Extract column from CSC matrix

Given a CSC matrix, which code snippet correctly extracts the second column as a dense array?

SciPy

from scipy.sparse import csc_matrix
import numpy as np

matrix = np.array([[0, 1, 0],
                   [2, 0, 3],
                   [0, 4, 0]])
csc = csc_matrix(matrix)

A csc[:, 1].toarray()

B csc.getcol(1).toarray().flatten()

C csc.getrow(1).toarray().flatten()

D csc[1, :].toarray()

💡 Hint

Use the method designed to get a column from a sparse matrix.

getcol(1) extracts the second column (index 1) as a sparse matrix.

Calling toarray() converts it to a dense 2D array.

flatten() converts it to 1D array.

Option B returns a 2D array but is valid too, but option B matches the exact requested output (1D array).

Options A and C extract rows, not columns.

🧠 Conceptual

expert

Memory efficiency of CSC vs CSR for column slicing

Which statement best explains why CSC format is more efficient than CSR format for extracting columns from a sparse matrix?

A CSC stores data row-wise, so column slicing is slower than CSR which stores data column-wise.

B CSR stores data row-wise, so column slicing requires scanning all rows, making it slower and less memory efficient.

C CSC stores data column-wise, so column slicing accesses contiguous memory, making it faster and more memory efficient.

D CSR and CSC have identical memory layouts, so there is no difference in efficiency for column slicing.

💡 Hint

Think about how data is stored and accessed in CSC vs CSR formats.

CSC format stores non-zero elements column by column, so accessing a column is direct and efficient.

CSR stores data row by row, so extracting a column requires scanning multiple rows, which is slower.

Therefore, CSC is more efficient for column slicing.

Practice

1. What does the CSC format in scipy.sparse primarily store for a sparse matrix?

easy

A. Only non-zero values and their row indices, organized by columns

B. All values including zeros, organized by rows

C. Only zero values and their column indices

D. All values including zeros, organized by columns

Solution

1. Step 1: Understand CSC format storage

   CSC stands for Compressed Sparse Column, which stores only non-zero values and their row indices, grouped by columns.

2. Step 2: Compare options with CSC definition

   Only non-zero values and their row indices, organized by columns matches the CSC format definition exactly, while others include zeros or wrong organization.

3. Final Answer:

   Only non-zero values and their row indices, organized by columns -> Option A

4. Quick Check:

   CSC stores non-zero values by columns = A [OK]

Hint: CSC stores non-zero values by columns only [OK]

Common Mistakes:

• Thinking CSC stores zero values
• Confusing CSC with CSR (row-based)
• Assuming all values are stored

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

easy

A. scipy.sparse.csc_matrix(arr)

B. scipy.sparse.csr_matrix(arr)

C. scipy.sparse.dense_matrix(arr)

D. scipy.sparse.csc(arr)

Solution

1. Step 1: Identify correct SciPy function for CSC

   The function to create a CSC matrix is scipy.sparse.csc_matrix().

2. Step 2: Check options for syntax correctness

   scipy.sparse.csc_matrix(arr) uses the correct function and syntax. scipy.sparse.csr_matrix(arr) creates CSR, not CSC. Options C and D are invalid functions.

3. Final Answer:

   scipy.sparse.csc_matrix(arr) -> Option A

4. Quick Check:

   Use csc_matrix() to create CSC format [OK]

Hint: Use csc_matrix() to create CSC sparse matrix [OK]

Common Mistakes:

• Using csr_matrix instead of csc_matrix
• Trying non-existent functions like dense_matrix
• Missing _matrix suffix in function name

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

import numpy as np
from scipy.sparse import csc_matrix

arr = np.array([[0, 0, 3],
                [4, 0, 0],
                [0, 5, 6]])
csc_matrix = csc_matrix(arr)

medium

A. [0 2 3 4]

B. [0 1 2 3]

C. [0 1 3 4]

D. [0 1 2 4]

Solution

1. Step 1: Understand indptr in CSC format

   indptr array shows column start indices in data arrays. For 3 columns, length is 4.

2. Step 2: Count non-zero elements per column

   Column 0 has 1 non-zero (4), column 1 has 1 non-zero (5), column 2 has 2 non-zeros (3,6). So indptr = [0,1,2,4].

3. Final Answer:

   [0 1 2 4] -> Option D

4. Quick Check:

   indptr counts cumulative non-zeros per column = B [OK]

Hint: Count non-zeros per column cumulatively for indptr [OK]

Common Mistakes:

• Counting rows instead of columns
• Mixing up indptr with indices array
• Off-by-one errors in cumulative counts

4. Identify the error in this code snippet that tries to create a CSC matrix:

from scipy.sparse import csc_matrix

arr = [[1, 0], [0, 2]]
csc = csc_matrix(arr, shape=(3,3))
print(csc.toarray())

medium

A. toarray() method does not exist for csc_matrix

B. Input array must be a NumPy array, not a list

C. Shape parameter is larger than input array size causing mismatch

D. csc_matrix requires data type float, not int

Solution

1. Step 1: Check input array and shape parameter

   Input array is 2x2 but shape is set to 3x3, causing dimension mismatch.

2. Step 2: Understand effect of shape mismatch

   Specifying a larger shape than data size is invalid and raises an error.

3. Final Answer:

   Shape parameter is larger than input array size causing mismatch -> Option C

4. Quick Check:

   Shape must match input size or smaller [OK]

Hint: Shape must match or be smaller than input array size [OK]

Common Mistakes:

• Assuming lists are invalid input
• Thinking data type must be float
• Believing toarray() is missing

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

hard

A. Convert to dense array and sum all values using np.sum()

B. Convert to CSC format and sum non-zero values column-wise using .sum(axis=0)

C. Convert to CSR format and sum non-zero values row-wise using .sum(axis=1)

D. Use COO format and iterate over all entries to sum columns manually

Solution

1. Step 1: Understand CSC format advantage

   CSC stores data column-wise, making column operations like sum efficient.

2. Step 2: Choose best method for column sums

   Using .sum(axis=0) on CSC matrix efficiently sums columns without converting to dense.

3. Final Answer:

   Convert to CSC format and sum non-zero values column-wise using .sum(axis=0) -> Option B

4. Quick Check:

   CSC + sum(axis=0) = fast column sums [OK]

Hint: Use CSC and sum(axis=0) for fast column sums [OK]

Common Mistakes:

• Using CSR which is row-based for column sums
• Converting to dense wastes memory
• Manually iterating instead of vectorized sum