https://github.com/JuliaMath/QuadGK.jl

adaptive 1d numerical Gauss–Kronrod integration in Julia
https://github.com/JuliaMath/QuadGK.jl

integration julia math numerical-integration quadrature

Last synced: 3 months ago
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adaptive 1d numerical Gauss–Kronrod integration in Julia

• Host: GitHub
• URL: https://github.com/JuliaMath/QuadGK.jl
• Owner: JuliaMath
• License: mit
• Created: 2016-12-20T03:38:54.000Z (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2024-08-02T00:16:19.000Z (3 months ago)
• Last Synced: 2024-08-02T17:44:53.926Z (3 months ago)
• Topics: integration, julia, math, numerical-integration, quadrature
• Language: Julia
• Homepage:
• Size: 595 KB
• Stars: 255
• Watchers: 9
• Forks: 36
• Open Issues: 8
• Metadata Files:
  • Readme: README.md
  • Funding: .github/FUNDING.yml
  • License: LICENSE
  • Citation: CITATION.bib

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• awesome-sciml - JuliaMath/QuadGK.jl: adaptive 1d numerical Gauss–Kronrod integration in Julia

README

        
# QuadGK.jl

[![Coverage Status](https://coveralls.io/repos/github/JuliaMath/QuadGK.jl/badge.svg?branch=master)](https://coveralls.io/github/JuliaMath/QuadGK.jl?branch=master)

Documentation:

[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://JuliaMath.github.io/QuadGK.jl/stable)

[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://JuliaMath.github.io/QuadGK.jl/dev)

This package provides support for one-dimensional numerical integration in Julia using adaptive

Gauss-Kronrod quadrature.

The code was originally part of Base Julia.  It supports integration of arbitrary numeric types,

including arbitrary precision (`BigFloat`), and even integration of arbitrary normed vector spaces

(e.g. matrix-valued integrands).

The package provides three basic functions: `quadgk`, `gauss`, and `kronrod`.

`quadgk` performs the integration, `gauss` computes Gaussian quadrature points and weights for integrating

over the interval [a, b], and `kronrod` computes Kronrod points, weights, and embedded Gaussian quadrature

weights for integrating over [-1, 1].   Typical usage looks like:

```jl

using QuadGK

integral, err = quadgk(x -> exp(-x^2), 0, 1, rtol=1e-8)

```

which computes the integral of exp(–x²) from x=0 to x=1 to a relative tolerance of 10⁻⁸, and returns the approximate `integral = 0.746824132812427` and error estimate `err = 7.887024366937112e-13` (which is actually smaller than the requested tolerance: convergence was very rapid because the integrand is smooth).

For more information, see the [documentation](https://JuliaMath.github.io/QuadGK.jl/stable).