CSC format (Compressed Sparse Column) in SciPy - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does CSC stand for in sparse matrix storage?

CSC stands for Compressed Sparse Column. It is a way to store sparse matrices efficiently by compressing data column-wise.

intermediate

How does CSC format store the matrix data?

CSC stores three arrays: one for non-zero values, one for row indices of those values, and one for column pointers that mark where each column starts in the values array.

beginner

Why is CSC format useful in data science?

CSC format saves memory and speeds up column-based operations like matrix-vector multiplication, which is common in data science tasks.

beginner

Show a simple example of creating a CSC matrix using scipy.

You can create a CSC matrix with scipy.sparse.csc_matrix. For example:<br><pre>from scipy.sparse import csc_matrix
import numpy as np

# Create a dense matrix
dense = np.array([[0, 0, 1], [1, 0, 0], [0, 2, 0]])

# Convert to CSC format
csc = csc_matrix(dense)
print(csc)</pre>

intermediate

What is the difference between CSC and CSR formats?

CSC compresses columns and is efficient for column slicing and operations. CSR (Compressed Sparse Row) compresses rows and is better for row slicing and row-based operations.

What does the 'indptr' array in CSC format represent?

A Values of non-zero elements

B Column pointers marking start of each column in data array

C Row indices of non-zero elements

D Total number of non-zero elements

The 'indptr' array in CSC format shows where each column starts in the data array.

Which operation is CSC format especially efficient for?

A Row slicing and row-based matrix operations

B Dense matrix multiplication

C Column slicing and column-based matrix operations

D Sorting matrix elements

CSC format is designed to speed up column slicing and column-based operations.

In scipy, which function creates a CSC sparse matrix?

A scipy.sparse.lil_matrix()

B scipy.sparse.csr_matrix()

C scipy.sparse.dok_matrix()

D scipy.sparse.csc_matrix()

The function scipy.sparse.csc_matrix() creates a CSC format sparse matrix.

What is stored in the 'data' array of a CSC matrix?

A Non-zero values of the matrix

B Row indices of non-zero values

C Column pointers

D Zero values

The 'data' array holds the actual non-zero values of the sparse matrix.

Which format is better for fast row slicing?

A CSR (Compressed Sparse Row)

B CSC (Compressed Sparse Column)

C Dense matrix

D Diagonal matrix

CSR format compresses rows and is optimized for fast row slicing.

Explain how the CSC format stores a sparse matrix and why it is useful.

Think about how columns are compressed and what arrays are needed.

Describe the difference between CSC and CSR formats and when to use each.

Focus on which dimension is compressed and the typical operations.

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