Sparse direct solvers (spsolve) in SciPy - Mini Project: Build & Apply

Solving Sparse Linear Systems with spsolve

📖 Scenario: Imagine you work in engineering and need to solve a system of equations that models a network. The system is large but mostly zeros, so it is called sparse. Using special tools helps solve it quickly.

🎯 Goal: You will create a sparse matrix and a vector, then use spsolve from scipy.sparse.linalg to find the solution vector.

📋 What You'll Learn

Create a sparse matrix using scipy.sparse.csr_matrix with exact values

Create a vector b with exact values

Use spsolve to solve the system Ax = b

Print the solution vector x

💡 Why This Matters

🌍 Real World

Sparse linear systems appear in engineering, physics, and computer science when modeling networks, circuits, or physical systems with many variables but few connections.

💼 Career

Knowing how to solve sparse systems quickly is important for data scientists and engineers working with large datasets or simulations where performance matters.

1

Create the sparse matrix A

Create a sparse matrix called A using scipy.sparse.csr_matrix with these exact values: [[3, 0, 1], [0, 4, 0], [2, 0, 5]]

SciPy

from scipy.sparse import csr_matrix
# Create the sparse matrix A with the given values
# Your code here

Need a hint?

Use csr_matrix and pass the list of lists exactly as shown.

2

Create the vector b

Create a vector called b as a list with these exact values: [5, 8, 12]

SciPy

from scipy.sparse import csr_matrix
A = csr_matrix([[3, 0, 1], [0, 4, 0], [2, 0, 5]])
# Create the vector b with the given values
# Your code here

Need a hint?

Just create a list named b with the numbers 5, 8, and 12 in that order.

3

Solve the system using spsolve

Import spsolve from scipy.sparse.linalg and create a variable x by solving Ax = b using spsolve(A, b)

SciPy

from scipy.sparse import csr_matrix
A = csr_matrix([[3, 0, 1], [0, 4, 0], [2, 0, 5]])
b = [5, 8, 12]
# Import spsolve and solve Ax = b
# Your code here

Need a hint?

Remember to import spsolve and call it with A and b.

4

Print the solution vector x

Print the variable x to display the solution vector

SciPy

from scipy.sparse import csr_matrix
from scipy.sparse.linalg import spsolve
A = csr_matrix([[3, 0, 1], [0, 4, 0], [2, 0, 5]])
b = [5, 8, 12]
x = spsolve(A, b)
# Print the solution vector x
# Your code here

Need a hint?

Use print(x) to show the solution.