geomin 0.0.5

A Python library for manipulating, plotting and computing with polyhedral and ellipsoidal sets.

Geomin

Python library for manipulating, plotting and computing with polyhedral and ellipsoidal sets. It is a relatively thin wrapper around Pycddlib, including some utility functions for convenience.

Installation

(The following assume you have already created a Python virtual environment)

Option 1. Install directly from PyPI:

pip install geomin

This does assume some prerequisites for pycddlib have already been installed. See their documentation for more information.

Option 2. Clone the repo and from within its root, run

pip install .

Usage

Creation of polytopes

From inequalities

Use the Polyhedron.from_inequalities method to build a polyhedron $X$ from a system of linear inequalities

$$ X = { x \in \mathbb{R}^n \mid H x \le h }. $$

For example, to represent the system

$$ \begin{cases} x_1 \ge -1 \ x_2 \ge -1 \ x_1 + x_2 \le 1 \end{cases} $$

You would write

import geomin as gp
import numpy as np

H = np.vstack([-np.eye(2), np.ones((1,2))])
h = np.array([1., 1., 1.])
poly = gp.Polyhedron.from_inequalities(H, h)

From vertices

Alternatively, a polyhedron can be constructed as the convex hull of a list of vertices.

import geomin as gp
import numpy as np

verts = np.array([(0, 0), (1, 0), (0, 1)])
poly = gp.Polyhedron.from_generators(verts)

Creation of ellipsoids

An ellipsoid created as gp.Ellipsoid(Q, c) represents

$$ { x: (x - c)^\top Q (x - c) \leq 1 }. $$

The argument $c$ is optional and is assumed to be $0$ by default.

Plotting

We provide some functions for easy plotting of sets, built on Matplotlib. Check the examples folder for more.

import matplotlib.pyplot as plt

# basic usage
plot_polytope(poly)

# Or with some styling
plt.figure()

plot_polytope(
    poly,
    color="tab:green",  # base color
    alpha=0.5,          # transparency
)

plt.show()