an-cli

A command-line tool providing implementations of common numerical analysis algorithms. Calculate roots, derivatives, integrals, interpolations, and regressions directly from your terminal.

Non-verbose output is simplified in order to facilitate piping to other commands

Features

• Root Finding:
  • bisection: Find roots using the Bisection method.
  • newton: Find roots using the Newton-Raphson method.
• Differentiation:
  • differentiate: Approximate the derivative using forward, backward, or centered difference methods.
• Integration:
  • simpson: Approximate definite integrals using Simpson's rule.
• Interpolation & Regression:
  • lagrange: Perform Lagrange polynomial interpolation.
  • lsm: Perform Linear Least Squares regression.
• Output Options:
  • -v/--verbose: Display detailed calculation steps and intermediate results in tables.
  • -p/--plot: Generate and display a matplotlib plot for relevant methods (Bisection, Newton, Lagrange, LSM).

Installation

Prerequisites

• Python 3.10 or higher
• pip (Python's package installer, usually included with Python)
• git (optional, for cloning the source)

Option 1: Install from Source

1. Clone the repository:

   git clone https://github.com/araujoviana/an-cli 
   cd an-cli

2. Install the package using pip:

   pip install .

Option 2: Install using uv

1. Clone the repository:

   git clone https://github.com/araujoviana/an-cli 
   cd an-cli

2. Install the package using uv pip:

   uv pip install .

uv offers a faster and isolated virtual environment, which is ideal for development 🙂

Usage

The tool follows the structure an-cli <command> [options].

You can get help for the tool or specific commands:

an-cli --help
an-cli bisection --help

Examples

Bisection Method: Find the root of f(x) = x^3 - x - 1 between 0 and 2.

an-cli bisection -a 0 -b 2 -f "x**3 - x - 1"

Show details and plot:

an-cli bisection -a 0 -b 2 -f "x**3 - x - 1" -v -p --tolerance 0.0001

Newton-Raphson Method: Find the root of f(x) = cos(x) - x starting near 0.5.

an-cli newton -e 0.5 -f "cos(x) - x"

Show details using relative error criterion and plot:

an-cli newton -e 0.5 -f "cos(x) - x" -v -p -c relative -t 1e-6

Differentiation: Find the derivative of f(x) = sin(x) at x = pi/4 using centered difference with h=0.01.

an-cli differentiate -x 0.785398 -H 0.01 -f "x ** 2" -m centered -v

Lagrange Interpolation: Interpolate y at x=2.5 given points (1,1), (2,4), (3,9).

an-cli lagrange -x 1,2,3 -y 1,4,9 -r 2.5 -v -p

Linear Least Squares: Find the regression line for points (1, 2), (2, 4.1), (3, 5.9), (4, 8.2) and estimate y at x=2.5.

an-cli lsm -x 1,2,3,4 -y 2,4.1,5.9,8.2 -r 2.5 -v -p

Simpson's Rule Integration: Integrate f(x) = x**2 from 0 to 1.

an-cli simpson -a 0 -b 1 -f "x**2" -v

License

This project is licensed under the MIT License. See the LICENSE file for details.