ellipsoidInclusion

Build Status

This is a c++ implementation of a function that checks the inclusion of one n-ellipsoid in 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 following code fragment tests the inclusion $E(P,c) \subseteq E(P_0,c_0) $

    double c[n] = {1.5, 1.5};
    double P[n][n] = {{4.0, 0.5},       
                 {0.5, 6.0}};
    double c0[n] = {1.6, 1.4};
    double P0[n][n] = {{0.4, -0.1},
                   {-0.1, 0.5}};

    if ellincheck(c, *P, c0, *P0, n){
     // do stuff
    }

Classes can also be defined as follows:

  ellipsoid el(P, c);
  ellipsoid el0(P0, c0);

  el.included_in(el0)

where P and P0 must be arma::mat and c and c0 must be arma::vec (check the Armadillo c++ library for more details on these types).

The method implemented in this library is 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},
}