Ellipsoids.jl

Build Status

This is a Julia implementation of this C++ library.

This module implements a functions that checks the inclusion and intersection of one $n$-ellipsoid with another. For a positive definite matrix $P\succ0\in\mathbb{R}^{n\times n}$ and a vector $c\in\mathbb{R}^{n}$, an ellipsoid shaped by $P$ and cetered at $c$ is defined as $E(P,c) := \{x\in\mathbb{R}^{n}:(x-c)^\top P(x-c)\leq 1\}$.

The method and examples implemented in this library are available in this paper. Please, cite it as:

@misc{calbert2022efficient,
  doi = {10.48550/ARXIV.2211.06237},
  url = {https://arxiv.org/abs/2211.06237},
  author = {Calbert, Julien and Egidio, Lucas N. and Jungers, Raphaël M.},
  title = {An Efficient Method to Verify the Inclusion of Ellipsoids},
  publisher = {preprint (arXiv)},
  year = {2022},
}

Some examples are still written in Python and some help rewriting them in Julia would be appreciated.