gaussquad

A mini-package to compute Gauss quadrature nodes and weights for arbitrary weight functions on finite intervals using the Golub–Welsch algorithm.

Based on:

• Golub & Welsch (1969)
• Technical report (1967)

Documentation is available at thatmariia.github.io/gaussquad

Features

• Compute quadrature nodes and weights for custom weight functions
• Use them directly to approximate integrals

Installation

From PyPI:

pip install gaussquad

From GitHub:

pip install git+https://github.com/thatmariia/gaussquad.git

Requirements: Python 3.13 or newer, numpy, scipy

Usage

You can integrate x^2 * w(x) from 0 to 5 with a weight function w(x)=exp(-x):

import numpy as np
from gaussquad import wquad

result = wquad(
    fn=lambda x: x**2,
    weight_fn=lambda x: np.exp(-x),
    interval=(0, 5),
    degree=5,
    moment_method="legendre"  # approximation for moments
)

print(f"Integral of x^2 from 0 to 5 with weight function exp(-x): {result}")  # ≈ 1.7507

More examples: docs » usage.md.

Development & docs

git clone https://github.com/thatmariia/gaussquad.git
cd gaussquad
python -m venv venv
source venv/bin/activate  # or venv\Scripts\activate on Windows

pip install -e ".[dev,docs]"

Citation

If you use this package in your research, please cite it using the information under "Cite this repository" on the right side of the GitHub page.

If you need a version-specific citation, you can find it on Zenodo.

License

This project is licensed under the Apache-2.0 License. See the LICENSE file for details.