Python中的多面体和多面体操作
项目描述
该库实现了凸多面体上的常见操作，例如多面体投影、双重描述（半空间和顶点表示之间的转换）、计算切比雪夫中心等。
有关详细信息，请参阅完整的API 文档。
例子
顶点枚举
我们可以通过A * x <= b计算以半空间表示形式描述的多面体的顶点列表：
import numpy
import pypoman
A = numpy.array([
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1],
[1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1],
[1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0],
[0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0],
[0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1]])
b = numpy.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 2, 2, 1, 2, 3])
vertices = pypoman.compute_polytope_vertices(A, b)多面体投影
让我们在x = [x_1 ... x_n] 上将一个 n 维多面体投影到它的前两个坐标proj(x) = [x_1 x_2]上：
import pypoman
from numpy import array, eye, ones, vstack, zeros
n = 10 # dimension of the original polytope
p = 2 # dimension of the projected polytope
# Original polytope:
# - inequality constraints: \forall i, |x_i| <= 1
# - equality constraint: sum_i x_i = 0
A = vstack([+eye(n), -eye(n)])
b = ones(2 * n)
C = ones(n).reshape((1, n))
d = array([0])
ineq = (A, b) # A * x <= b
eq = (C, d) # C * x == d
# Projection is proj(x) = [x_0 x_1]
E = zeros((p, n))
E[0, 0] = 1.
E[1, 1] = 1.
f = zeros(p)
proj = (E, f) # proj(x) = E * x + f
vertices = pypoman.project_polytope(proj, ineq, eq, method='bretl')
if __name__ == "__main__": # plot projected polytope
import pylab
pylab.ion()
pylab.figure()
pypoman.plot_polygon(vertices)
