dualdesc 0.1.0

Dual description of polytopes.

dualdesc

Dual description for polytopes. A wrapper around pycddlib. Mainly for easily converting between H- and V-representations. No utilities for facet enumeration, adjacencies, etc.

Usage

This package contains two classes, HRepr and VRepr, for the H- and V-representations of polytopes. They have methods to_v() and to_h(), respectively, for converting between them.

HRepr(Au, bu, Ae, be) represents the polytope defined by all points x s.t. Au @ x <= bu and Ae @ x == be. Au, bu (inequality constraints) and Ae, be (equality constraints) are also fields on the HRepr object. If there are nu inequality and ne equality constraints, and the ambient dimension is d, the shapes of these matrices are:

• Au: (nu, d)
• bu: (d,)
• Ae: (ne, d)
• be: (d,)

VRepr(Vc, Vn, Vl) represents the polytope defined by conv(Vc) + nonneg(Vn) + linspace(Vl), where conv is the convex combination of a set of points, nonneg is non-negative linear combinations of a set of points, linspace is a linear combination of a set of points, and + is Minkowski addition.

A simple example

The example below defines an unbounded (i.e. non-null cone part) polytope with 3 facets and 2 vertices:

import numpy as np
import dualdesc as dd

M = np.array([
	[1, 0, 1], # x0        <= 1
	[0, 2, 1], #      2 x1 <= 1
	[1, 1, 1], # x0 +   x1 <= 1
], dtype = np.float64)
Au = M[:,:2]
bu = M[:,-1]
h = dd.HRepr(Au, bu)
v = h.to_v()
# Vertices (conv component):
# 	v.Vc = [[0.5, 0.5], [1, 0]]
# Cone part (nonneg and linear components):
# 	v.Vn = [[-1, 0], [0, -1]]
# 	v.Vl = []

Why not pypoman?

pypoman has more features, but only supports bounded polytopes.

Why not use pycddlib directly?

pycddlib has more features (like adjacency lists), but is too low level and doesn't have a nice interface.