numroot 0.1.1

Numerical analysis solver for equations and optimization

NumRoot

Python package for numerical resolution of nonlinear equations with several numerical analysis methods.

🚀 Installation

pip install numroot

Development installation

pip install numroot[dev]

📖 Quick use

from numroot import NonlinearSolver

# Create a solver object
solver = NonlinearSolver()

# Define a function to analyse (example: x² - 2 = 0)
def f(x):
    return x**2 - 2

# Bissection method
result = solver.bisection(f, x_a=0, x_b=2, epsilon=1e-6)
print(f"Root found: {result.root}")  # ≈ 1.414
print(f"Number of iterations: {result.iterations}")

# Newton-Raphson method
def df(x):
    return 2*x

result = solver.newton_raphson(f, df, x_0=1.5, epsilon=1e-6)
print(f"Root found: {result.root}")  # ≈ 1.414
print(f"Number of iterations: {result.iterations}")

# Secant method
result = solver.secant(f, x_0=1.0, x_1=2.0, epsilon=1e-6)
print(f"Root found: {result.root}")  # ≈ 1.414
print(f"Number of iterations: {result.iterations}")

🔧 Available methods

Bissection method

• Advantages: Always convergent, robust
• Disadvantages: Slow convergence
• Usage: When you have an interval [a,b] where f(a) and f(b) have opposite signs

result = solver.bisection(func, a, b, epsilon=1e-6, maxiter=100)

Newton-Raphson method

• Advantages: Very fast quadratic convergence
• Disadvantages: Requires derivative, may diverge
• Usage: When you know the derivative and have a good initial estimate

result = solver.newton_raphson(func, dfunc, x0, epsilon=1e-6, maxiter=100)

Secant method

• Advantages: No derivative needed, super-linear convergence
• Disadvantages: Can be unstable with bad initial points.
• Uses: Compromise between bisection and Newton-Raphson

result = solver.secant(func, x0, x1, epsilon=1e-6, maxiter=100)

🎯 Typical use cases

• Solving physical equations (trajectories, oscillations)
• Engineering calculations (balance points, intersections)
• Mathematical modeling (zeros of complex functions)
• Research and education in numerical analysis

📋 Requirements

• Python 3.8+
• NumPy >= 1.20.0

🔗 Links

• Documentation complète
• PyPI
• Issues GitHub
• Code source

📈 Roadmap

• Systems of non-linear equations
• Ordinary differential equations
• Numerical optimization
• Graphical interface
• Interactive visualizations

📚 References

• Geeks for Geeks - Secant method
• Math Libretexts - Bisection Method
• Math Libretexts - Newton-Raphson Method