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https://github.com/friesischscott/minimumvolumeellipsoids.jl
Calculation and uniform sampling of minimum-volume enclosing ellipsoids
https://github.com/friesischscott/minimumvolumeellipsoids.jl
ellipsoids julia uniform-sampling
Last synced: about 2 months ago
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Calculation and uniform sampling of minimum-volume enclosing ellipsoids
- Host: GitHub
- URL: https://github.com/friesischscott/minimumvolumeellipsoids.jl
- Owner: FriesischScott
- License: mit
- Created: 2021-10-13T13:34:07.000Z (about 3 years ago)
- Default Branch: master
- Last Pushed: 2021-12-21T15:37:36.000Z (about 3 years ago)
- Last Synced: 2024-10-09T23:28:12.204Z (2 months ago)
- Topics: ellipsoids, julia, uniform-sampling
- Language: Julia
- Homepage:
- Size: 80.1 KB
- Stars: 6
- Watchers: 3
- Forks: 2
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
README
# MinimumVolumeEllipsoids.jl
[](https://github.com/FriesischScott/MinimumVolumeEllipsoids.jl/actions/workflows/ci.yml)
[](https://codecov.io/gh/FriesischScott/MinimumVolumeEllipsoids.jl)
MinimumVolumeEllipsoids.jl is a Julia module which implements algorithms to compute Minimum-Volume Ellipsoids (MVE) from given data. The algorithms are implemented as defined in _Minimum-volume ellipsoids: Theory and algorithms_ by Michael J. Todd. The code has been adapted from the original Matlab implementation supplied with the book. For the original code see here: http://archive.siam.org/books/mo23/
In addition to computing the MVE this module also includes a function to sample uniformly over the ellipsoid using an algorithm proposed by Dezert & Musso.
## Usage
To compute the minimum-volume enclosing ellipsoid centered at the origin for a set of four points run the following code:
```julia
using MinimumVolumeEllipsoids
X = [
-1 -1 1 2
1 -1 -1 2
]
ϵ = minimum_volume_ellipsoid(X, centered=true)
```
This results in an ellipsoid with the center `ϵ.x`
```julia
2-element Vector{Float64}:
0.0
0.0
```
and the shape matrix `ϵ.H`
```julia
2×2 PDMat{Float64, Matrix{Float64}}:
0.625 -0.375
-0.375 0.625
```
To relax the centered condition an compute the optimal minimum-volume enclosing ellipsoid simply omit the `centered` keyword
```julia
ϵ = minimum_volume_ellipsoid(X)
```
To create uniform random samples over either ellipsoid simply run
```julia
U = rand(ϵ, 1000)
```
## References
Dezert, J., & Musso, C. (2001). An efficient method for generating points uniformly distributed in hyperellipsoids. In _Proceedings of the Workshop on Estimation, Tracking and Fusion: A Tribute to Yaakov Bar-Shalom_.
Todd, M. J. (2016). _Minimum-volume ellipsoids: Theory and algorithms_. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/1.9781611974386