CSC format (Compressed Sparse Column) in SciPy - Mini Project: Build & Apply

Working with CSC format (Compressed Sparse Column) in SciPy

📖 Scenario: You have a sparse matrix representing connections between users and items in a recommendation system. Sparse matrices save memory by storing only non-zero values.One common way to store sparse matrices is the CSC (Compressed Sparse Column) format, which stores data column-wise efficiently.

🎯 Goal: You will create a sparse matrix in COO format, convert it to CSC format, and then extract the data arrays that represent the CSC structure.

📋 What You'll Learn

Create a COO sparse matrix with given data, row indices, and column indices

Create a variable for the shape of the matrix

Convert the COO matrix to CSC format

Extract the data, indices, and indptr arrays from the CSC matrix

Print the extracted arrays

💡 Why This Matters

🌍 Real World

Sparse matrices are used in recommendation systems, natural language processing, and scientific computing where data is mostly zeros. CSC format helps efficiently store and process such data.

💼 Career

Data scientists and machine learning engineers often work with sparse data. Understanding CSC format helps optimize memory and speed when handling large datasets.

1

Create a COO sparse matrix

Import coo_matrix from scipy.sparse. Create a COO sparse matrix called coo with data = [10, 20, 30, 40], row = [0, 1, 2, 0], and col = [0, 2, 2, 1]. Set the shape to (3, 3).

SciPy

# Import coo_matrix and create the COO sparse matrix coo
# Your code here

Hint

Use coo_matrix((data, (row, col)), shape=(3, 3)) to create the sparse matrix.

2

Set the shape variable

Create a variable called shape and set it to the tuple (3, 3) representing the matrix shape.

SciPy

from scipy.sparse import coo_matrix

data = [10, 20, 30, 40]
row = [0, 1, 2, 0]
col = [0, 2, 2, 1]
coo = coo_matrix((data, (row, col)), shape=(3, 3))

# Create a variable called shape and set it to (3, 3)
# Your code here

Hint

Just assign the tuple (3, 3) to the variable shape.

3

Convert COO to CSC format and extract arrays

Convert the COO matrix coo to CSC format and store it in a variable called csc. Then extract the data, indices, and indptr arrays from csc and store them in variables called data_csc, indices_csc, and indptr_csc respectively.

SciPy

from scipy.sparse import coo_matrix

data = [10, 20, 30, 40]
row = [0, 1, 2, 0]
col = [0, 2, 2, 1]
coo = coo_matrix((data, (row, col)), shape=(3, 3))

shape = (3, 3)

# Convert coo to csc format and extract data, indices, indptr arrays
# Your code here

Hint

Use tocsc() method to convert. Access data, indices, and indptr attributes from the CSC matrix.

4

Print the CSC arrays

Print the variables data_csc, indices_csc, and indptr_csc each on a separate line.

SciPy

from scipy.sparse import coo_matrix

data = [10, 20, 30, 40]
row = [0, 1, 2, 0]
col = [0, 2, 2, 1]
coo = coo_matrix((data, (row, col)), shape=(3, 3))

shape = (3, 3)

csc = coo.tocsc()
data_csc = csc.data
indices_csc = csc.indices
indptr_csc = csc.indptr

# Print data_csc, indices_csc, and indptr_csc each on a new line
# Your code here

Hint

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

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