Why sparse matrices save memory in SciPy - Test Your Understanding

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a sparse matrix from a dense matrix using SciPy.

SciPy

from scipy.sparse import [1]
dense_matrix = [[0, 0, 3], [4, 0, 0], [0, 0, 0]]
sparse_matrix = [1](dense_matrix)

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

Acsr_matrix

Blist

Cmatrix

Darray

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'array' or 'list' instead of a sparse matrix constructor.

Trying to create a sparse matrix without importing the correct function.

The csr_matrix function from SciPy creates a sparse matrix from a dense matrix efficiently.

2fill in blank

medium

Complete the code to get the number of non-zero elements in a sparse matrix.

SciPy

from scipy.sparse import csr_matrix
sparse_matrix = csr_matrix([[0, 0, 3], [4, 0, 0], [0, 0, 0]])
non_zero_count = sparse_matrix.[1]

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Ashape

Bsize

Ccount

Dnnz

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'size' which gives total elements, not just non-zero.

Using 'shape' which gives matrix dimensions.

The nnz attribute gives the number of non-zero elements in a sparse matrix.

3fill in blank

hard

Fix the error in the code to convert a sparse matrix back to a dense array.

SciPy

from scipy.sparse import csr_matrix
sparse_matrix = csr_matrix([[0, 0, 3], [4, 0, 0], [0, 0, 0]])
dense_array = sparse_matrix.[1]()

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Atoarray

Btodense

Cto_list

Dto_numpy

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'todense' which returns a matrix, not an array.

Using non-existent methods like 'to_list' or 'to_numpy'.

The toarray() method converts a sparse matrix to a dense NumPy array.

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.

SciPy

{word: [1] for word in words if [2]

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Alen(word)

Blen(word) > 3

Cword

Dword > 3

Attempts:

3 left

💡 Hint

Common Mistakes

Using the word itself as the value instead of its length.

Using the word in the condition instead of its length.

The dictionary comprehension maps each word to its length using len(word) and filters words with length greater than 3 using len(word) > 3.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps uppercase words to their counts only if count is greater than 0.

SciPy

{ [1]: [2] for [3], [2] in data.items() if [2] > 0 }

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Ak.upper()

Bv

Ck

Ditem

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'item' instead of 'k' and 'v'.

Not converting the key to uppercase.

The comprehension maps uppercase keys k.upper() to their values v for each key k and value v in data.items(), filtering values greater than 0.

Practice

1. Why do sparse matrices save memory compared to regular dense matrices?

easy

A. Because they store only the non-zero elements and their positions

B. Because they compress all data into a single number

C. Because they convert numbers into strings

D. Because they store all elements including zeros explicitly

Solution

1. Step 1: Understand storage in dense matrices

   Dense matrices store every element, including zeros, which uses a lot of memory when many zeros exist.

2. Step 2: Understand storage in sparse matrices

   Sparse matrices store only non-zero values and their positions, saving memory by ignoring zeros.

3. Final Answer:

   Because they store only the non-zero elements and their positions -> Option A

4. Quick Check:

   Sparse matrices save memory by storing non-zero values only [OK]

Hint: Sparse = store only non-zero values and positions [OK]

Common Mistakes:

• Thinking sparse matrices store all zeros explicitly
• Confusing compression with sparse storage
• Believing sparse matrices convert numbers to strings

2. Which of the following is the correct way to create a sparse matrix using scipy?

easy

A. scipy.sparse.csr_matrix([[0, 0], [1, 0]])

B. scipy.sparse.dense_matrix([[0, 1], [0, 0]])

C. scipy.sparse.array([[1, 0], [0, 1]])

D. scipy.sparse.matrix([[0, 0], [0, 0]])

Solution

1. Step 1: Identify valid sparse matrix constructors in scipy

   scipy.sparse provides constructors like csr_matrix, csc_matrix, etc. 'csr_matrix' is a common sparse format.

2. Step 2: Check each option for correctness

   scipy.sparse.csr_matrix([[0, 0], [1, 0]]) uses csr_matrix correctly. Options B, C, and D use invalid or non-existent functions.

3. Final Answer:

   scipy.sparse.csr_matrix([[0, 0], [1, 0]]) -> Option A

4. Quick Check:

   Use csr_matrix to create sparse matrices [OK]

Hint: Use csr_matrix() to create sparse matrices [OK]

Common Mistakes:

• Using non-existent functions like dense_matrix or sparse.array
• Confusing sparse matrix constructors with dense matrix functions
• Forgetting to import scipy.sparse before use

3. What will be the output of this code?

import numpy as np
from scipy.sparse import csr_matrix

arr = np.array([[0, 0, 3], [4, 0, 0]])
sparse_mat = csr_matrix(arr)
print(sparse_mat.data)

medium

A. [0 0 3 4 0 0]

B. [0 3 4]

C. [3 4 0]

D. [3 4]

Solution

1. Step 1: Understand csr_matrix data attribute

   The 'data' attribute stores only the non-zero elements of the sparse matrix in row-major order.

2. Step 2: Identify non-zero elements in the array

   In arr, non-zero elements are 3 (at position [0,2]) and 4 (at position [1,0]).

3. Final Answer:

   [3 4] -> Option D

4. Quick Check:

   csr_matrix.data shows only non-zero values [OK]

Hint: csr_matrix.data shows only non-zero values [OK]

Common Mistakes:

• Expecting zeros to appear in sparse data
• Confusing data attribute with full matrix
• Misreading the order of stored elements

4. Find the error in this code that tries to create a sparse matrix:

from scipy.sparse import csr_matrix

matrix = csr_matrix([[0, 1], [2, 0]])
print(matrix.data)

medium

A. Missing import for numpy

B. csr_matrix cannot be created from a list of lists

C. No error, code runs correctly and prints non-zero values

D. csr_matrix requires dense matrix input, not list

Solution

1. Step 1: Check csr_matrix input types

   csr_matrix can accept a list of lists as input and convert it to sparse format.

2. Step 2: Verify code execution

   The code imports csr_matrix, creates a sparse matrix from a list, and prints non-zero data without error.

3. Final Answer:

   No error, code runs correctly and prints non-zero values -> Option C

4. Quick Check:

   csr_matrix accepts list input directly [OK]

Hint: csr_matrix accepts list of lists input [OK]

Common Mistakes:

• Assuming csr_matrix needs numpy arrays only
• Thinking missing numpy import causes error here
• Believing csr_matrix cannot handle lists

5. You have a large 10000x10000 matrix with 99% zeros. Which approach saves the most memory and why?

Option A: Store as a dense numpy array
Option B: Store as a scipy sparse matrix
Option C: Store as a list of lists including zeros
Option D: Store as a dictionary with all elements

hard

A. Option A, because numpy arrays are always memory efficient

B. Option B, because sparse matrices store only non-zero values and positions

C. Option C, because lists are flexible and fast

D. Option D, because dictionaries store keys and values explicitly

Solution

1. Step 1: Analyze memory use of dense numpy arrays

   Dense arrays store every element, so 10000x10000 elements use a lot of memory, including zeros.

2. Step 2: Analyze sparse matrix memory use

   Sparse matrices store only non-zero elements and their positions, greatly reducing memory when zeros dominate.

3. Step 3: Compare lists and dictionaries

   Lists of lists store all elements including zeros, using much memory. Dictionaries store keys and values, but overhead is high and all elements must be stored.

4. Final Answer:

   Option B, because sparse matrices store only non-zero values and positions -> Option B

5. Quick Check:

   Sparse matrices save memory with many zeros [OK]

Hint: Sparse matrices save memory by ignoring zeros [OK]

Common Mistakes:

• Assuming numpy arrays are always memory efficient
• Thinking lists or dictionaries save memory with many zeros
• Ignoring overhead of storing keys in dictionaries