quadproj 2.0.1

A package to project onto quadratic hypersurface.

quadproj

A simple library to project a point onto a quadratic surface, or quadric.

How to install quadproj?

It is a one-liner!

python3 -m pip install quadproj

See installation page for further information and the requirements.

Documentation

The documentation is hosted on GitLab: https://loicvh.gitlab.io/quadproj

How does quadproj work?

The projection is obtained by computing exhaustively all KKT point from the optimization problem defining the projection. The authors of [1] show that for non-cylindrical central quadrics, the solutions belong to the KKT points that consist in the intersection between:

• a unique root of a nonlinear function on a specific interval;
• a set of closed-form points.

Either set can be empty but for a nonempty quadric, at least one is nonempty and contains (one of the) projections.

The full explanation is provided in [1].

How to use quadproj?

See the quickstart page or the API documentation.

Dependencies

See requirements.txt.

[1]

(2021) L. Van Hoorebeeck, P.-A. Absil and A. Papavasiliou, “Projection onto quadratic hypersurfaces”, submitted. (preprint, abstract/BibTex)