QR decomposition in SciPy - Mini Project: Build & Apply

QR Decomposition with SciPy

📖 Scenario: You work as a data analyst and need to break down a matrix into simpler parts to understand its structure better. QR decomposition is a method that helps split a matrix into two parts: one with orthogonal columns and one upper triangular matrix. This is useful in solving systems of equations and data fitting.

🎯 Goal: Build a Python program that uses SciPy to perform QR decomposition on a given matrix and display the resulting matrices.

📋 What You'll Learn

Create a 3x3 matrix using NumPy with exact values

Set up a configuration variable to choose the mode of QR decomposition

Use SciPy's qr function to decompose the matrix

Print the Q and R matrices as output

💡 Why This Matters

🌍 Real World

QR decomposition is used in data fitting, solving linear systems, and simplifying matrix computations in engineering and science.

💼 Career

Understanding QR decomposition helps in roles like data analyst, data scientist, and engineer where matrix operations and numerical methods are common.

1

Create the matrix

Import NumPy as np and create a 3x3 matrix called A with these exact values: [[1, 2, 3], [4, 5, 6], [7, 8, 9]].

SciPy

import numpy as np
# Create the matrix A with the given values
# Your code here

Need a hint?

Use np.array to create the matrix with the exact values.

2

Set QR decomposition mode

Create a variable called mode and set it to the string 'reduced' to specify the QR decomposition mode.

SciPy

import numpy as np
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
# Set the mode variable to 'reduced'
# Your code here

Need a hint?

Assign the string 'reduced' to the variable mode.

3

Perform QR decomposition

Import the qr function from scipy.linalg and use it to decompose matrix A with the mode set by mode. Store the results in variables Q and R.

SciPy

import numpy as np
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
mode = 'reduced'
# Import qr from scipy.linalg and perform QR decomposition
# Your code here

Need a hint?

Use from scipy.linalg import qr and call qr(A, mode=mode).

4

Display the results

Print the matrices Q and R on separate lines using print statements.

SciPy

import numpy as np
A = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
mode = 'reduced'
from scipy.linalg import qr
Q, R = qr(A, mode=mode)
# Print Q and R matrices
# Your code here

Need a hint?

Use two print statements: one for Q and one for R.