quadproj 0.0.47

A package to project onto quadratic hypersurface.

quadproj

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

Please cite us if you use this package.

How to install quadproj?

python3 -m pip install quadproj

How does quadproj works?

Roughly speaking, the projection is obtained by computing exhaustively all KKT point from the optimization problem defining the projection. We show in [1] 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?

The class Quadric from the quadrics module allows to create a non-empty, non-cylindrical, and central quadric.

We can use the project function from the project module to find (one of) the projections of some point onto the quadric.

Dependencies

See requirements.txt.

[1]

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