Root finding (root, brentq) in SciPy - Mini Project: Build & Apply

Root Finding with scipy: Using root and brentq

📖 Scenario: Imagine you are an engineer trying to find the temperature at which a machine part reaches a specific stress level. This requires solving an equation where the stress equals zero. You will use Python's scipy library to find the root of this equation.

🎯 Goal: You will create a function representing the stress equation, then use scipy.optimize.root and scipy.optimize.brentq methods to find the temperature where the stress is zero.

📋 What You'll Learn

Create a function stress_equation that takes a variable T and returns T**3 - 6*T**2 + 11*T - 6

Create a variable initial_guess and set it to 2.5

Use scipy.optimize.root with stress_equation and initial_guess to find a root, store result in root_result

Use scipy.optimize.brentq with stress_equation and interval (1.5, 2.5) to find a root, store result in brentq_root

Print both roots with descriptive messages

💡 Why This Matters

🌍 Real World

Engineers and scientists often need to find where a function equals zero to understand critical points like stress, temperature, or pressure thresholds.

💼 Career

Root finding is a fundamental skill in data science and engineering roles, useful for solving equations that model real-world problems.

1

Create the stress equation function

Create a function called stress_equation that takes one argument T and returns the value of T**3 - 6*T**2 + 11*T - 6.

SciPy

# Define the stress_equation function
# Your code here

Need a hint?

This function models the stress depending on temperature T.

2

Set the initial guess for root finding

Create a variable called initial_guess and set it to 2.5.

SciPy

def stress_equation(T):
    return T**3 - 6*T**2 + 11*T - 6

# Set initial_guess to 2.5
# Your code here

Need a hint?

The initial guess helps the root finder start searching near this value.

3

Find roots using root and brentq methods

Import root and brentq from scipy.optimize. Use root with stress_equation and initial_guess, store the result in root_result. Then use brentq with stress_equation and interval (1.5, 2.5), store the result in brentq_root.

SciPy

def stress_equation(T):
    return T**3 - 6*T**2 + 11*T - 6

initial_guess = 2.5

# Import root and brentq from scipy.optimize
# Use root with stress_equation and initial_guess, save to root_result
# Use brentq with stress_equation and interval (1.5, 2.5), save to brentq_root
# Your code here

Need a hint?

Use root to find a root near the initial guess, and brentq to find a root in the interval (1.5, 2.5).

4

Print the roots found

Print the root found by root_result using root_result.x[0] with the message: Root found by root method:. Then print the root found by brentq_root with the message: Root found by brentq method:.

SciPy

from scipy.optimize import root, brentq

def stress_equation(T):
    return T**3 - 6*T**2 + 11*T - 6

initial_guess = 2.5

root_result = root(stress_equation, initial_guess)
brentq_root = brentq(stress_equation, 1.5, 2.5)

# Print the root from root_result.x[0] with message
# Print the root from brentq_root with message
# Your code here

Need a hint?

Use print and f-strings to show the roots clearly.