https://github.com/pabloferz/nintegration.jl
Multidimensional numerical integration in pure Julia
https://github.com/pabloferz/nintegration.jl
Last synced: 3 months ago
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Multidimensional numerical integration in pure Julia
- Host: GitHub
- URL: https://github.com/pabloferz/nintegration.jl
- Owner: pabloferz
- License: mit
- Created: 2017-03-27T00:13:26.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2020-06-14T04:39:18.000Z (almost 5 years ago)
- Last Synced: 2025-01-23T03:26:04.953Z (5 months ago)
- Language: Julia
- Size: 36.1 KB
- Stars: 20
- Watchers: 5
- Forks: 1
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
- License: LICENSE.md
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README
# NIntegration.jl
[![Build Status][travis-img]][travis-url] [![Coverage Status][coveral-img]][coveral-url] [![Coverage Status][codecov-img]][codecov-url]
This is library intended to provided multidimensional numerical integration
routines in pure [Julia](http://julialang.org)
## Status
For the time being this library can only perform integrals in three dimensions.
**TODO**
- [ ] Add rules for other dimensions
- [ ] Make sure it works properly with complex valued functions
- [ ] Parallelize
- [ ] Improve the error estimates (the [Cuba library](http://www.feynarts.de/cuba/) and consequently [Cuba.jl](https://github.com/giordano/Cuba.jl) seem to calculate tighter errors)
## Installation
`NIntegration.jl` should work on Julia 1.0 and later versions and can be
installed from a Julia session by running
```julia
julia> using Pkg
julia> Pkg.add(PackageSpec(url = "https://github.com/pabloferz/NIntegration.jl.git"))
```
## Usage
Once installed, run
```julia
using NIntegration
```
To integrate a function `f(x, y, z)` on the
[hyperrectangle](https://en.wikipedia.org/wiki/Hyperrectangle) defined by
`xmin` and `xmax`, just call
```julia
nintegrate(
f::Function, xmin::NTuple{N}, xmax::NTuple{N};
reltol = 1e-6, abstol = eps(), maxevals = 1000000
)
```
The above returns a tuple `(I, E, n, R)` of the calculated integral `I`, the
estimated error `E`, the number of integrand evaluations `n`, and a list `R` of
the subregions in which the integration domain was subdivided.
If you need to evaluate multiple functions `(f₁, f₂, ...)` on the same
integration domain, you can evaluate the function `f` with more "features" and
use its subregions list to estimate the integral for the rest of the functions
in the list, e.g.
```julia
(I, E, n, R) = nintegrate(f, xmin, xmin)
I₁ = nintegrate(f₁, R)
```
## Technical Algorithms and References
The integration algorithm is based on the one decribed in:
* J. Berntsen, T. O. Espelid, and A. Genz, "An Adaptive Algorithm for the
Approximate Calculation of Multiple Integrals," *ACM Trans. Math. Soft.*, 17
(4), 437-451 (1991).
## Author
* [Pablo Zubieta](https://github.com/pabloferz)
## Acknowdlegments
The author expresses his gratitude to [Professor Alan
Genz](http://www.math.wsu.edu/faculty/genz/homepage) for some useful pointers.
This work was financially supported by CONACYT through grant 354884.
[//]: # (Links)
[travis-img]: https://travis-ci.org/pabloferz/NIntegration.jl.svg?branch=master
[travis-url]: https://travis-ci.org/pabloferz/NIntegration.jl
[coveral-img]: https://coveralls.io/repos/pabloferz/NIntegration.jl/badge.svg?branch=master&service=github
[coveral-url]: https://coveralls.io/github/pabloferz/NIntegration.jl?branch=master
[codecov-img]: http://codecov.io/github/pabloferz/NIntegration.jl/coverage.svg?branch=master
[codecov-url]: http://codecov.io/github/pabloferz/NIntegration.jl?branch=master