zonopy.zonotope

class zonopy.zonotope(Z, dtype=None, device=None)

Bases: object

1D Zonotope class

A Zonotope is a set of the form

$$\mathcal{Z} := \left\{c + \sum_{i=1}^{N} a_i g_i \; \middle\vert \; a_i \in [-1,1]\right\}$$

where $c$ is the center and $g_i$ are the generators, each of which is a vector in the same space as $c$.

This class defines a basic zonotope and its operations. $\mathbf{Z}$ is a tensor of shape $(N+1) \times d$ where $N$ is the number of generators and $d$ is the dimension of the zonotope. The first row of $Z$ is the center and the rest are the generators, such that $\mathbf{Z} = [c,G]^T$. $G = [g_1, g_2, \ldots, g_N]$ is a matrix of shape $N \times d$.

__init__(Z, dtype=None, device=None)

Initialize a zonotope

Parameters:

• Z (torch.Tensor) – center vector and generator matrix $\mathbf{Z} = [c,G]^T$

• dtype (torch.dtype, optional) – data type of $\mathbf{Z}$. If None, the data type is inferred. Defaults to None.

• device (str, optional) – device of $\mathbf{Z}$. If None, the device is inferred. Defaults to None.

Raises:

AssertionError – If the dimension of $\mathbf{Z}$ is not 2

Methods

__init__(Z[, dtype, device])	Initialize a zonotope
cpu()	Change the device of a zonotope to CPU
deleteZerosGenerators([eps])	Delete zero vector generators return <zonotope>
plot(ax[, facecolor, edgecolor, linewidth, dim])	plot 2 dimensional projection of a zonotope self: <zonotope> ax: <Axes> axes oject of a figure to plot facecolor: <string> color of face edgecolor: <string> color of edges
polygon()	Vertice representation as a polygon from a 2-dimensional zonotope
polygon_patch([alpha, facecolor, edgecolor, ...])
polyhedron()	Vertice representation as a polygon from a 3-dimensional zonotope
polyhedron_patch([alpha, facecolor, ...])
polytope([combs])	Half-plane representation of zonotope return, A: <torch.tensor>, shape [,nx] b: <torch.tensor>, shape []
project([dim])	The projection of a zonotope onto the specified dimensions self: <zonotope> dim: <int> or <list> or <torch.Tensor> dimensions for prjection
reduce(order[, option])
slice(slice_dim, slice_pt)	slice zonotope on specified point in a certain dimension self: <zonotope> slice_dim: <torch.Tensor> or <list> or <int> , shape [] slice_pt: <torch.Tensor> or <list> or <float> or <int> , shape [] return <zonotope>
to([dtype, device])	Change the device and data type of a zonotope dtype: torch.float or torch.double device: 'cpu', 'gpu', 'cuda:0', ...
to_interval()	Convert zonotope to interval return <interval>
to_polyZonotope([dim, id])	Convert zonotope to polynomial zonotope self: <zonotope> dim: <int>, dimension to take as sliceable return <polyZonotope>

Attributes

center	The center of a zonotope return <torch.Tensor> , shape [nx]
device	The device of a zonotope properties return 'cpu', 'cuda:0', or ...
dimension	The dimension of a zonotope return <int>, nx
dtype	The data type of a zonotope properties return torch.float or torch.double
generators	Generators of a zonotope return <torch.Tensor> , shape [N, nx]
n_generators	The number of generators of a zonotope return <int>, N
shape	The shape of vector elements (ex.

property center

The center of a zonotope return <torch.Tensor> , shape [nx]

cpu()

Change the device of a zonotope to CPU

deleteZerosGenerators(eps=0)

Delete zero vector generators return <zonotope>

property device

The device of a zonotope properties return ‘cpu’, ‘cuda:0’, or …

property dimension

The dimension of a zonotope return <int>, nx

property dtype

The data type of a zonotope properties return torch.float or torch.double

property generators

Generators of a zonotope return <torch.Tensor> , shape [N, nx]

property n_generators

The number of generators of a zonotope return <int>, N

plot(ax, facecolor='none', edgecolor='green', linewidth=0.2, dim=[0, 1])

plot 2 dimensional projection of a zonotope self: <zonotope> ax: <Axes> axes oject of a figure to plot facecolor: <string> color of face edgecolor: <string> color of edges

ex. import matplotlib.pyplot as plt fig = plt.figure() ax = fig.gca() zono.plot(ax) plt.show()

polygon()

Vertice representation as a polygon from a 2-dimensional zonotope

return <torch.Tensor>, <torch.float> or <torch.double> , shape [P,2], where P is the number of vertices

polygon_patch(alpha=0.5, facecolor='none', edgecolor='green', linewidth=0.2, dim=[0, 1])

polyhedron()

Vertice representation as a polygon from a 3-dimensional zonotope

return <torch.Tensor>, <torch.float> or <torch.double> , shape [P,3], where P is the number of vertices

polyhedron_patch(alpha=0.5, facecolor='none', edgecolor='green', linewidth=0.2)

polytope(combs=None)

Half-plane representation of zonotope return, A: <torch.tensor>, shape [,nx] b: <torch.tensor>, shape []

A point, x (torch.Tensor, shape (nx,)), is at outside of a zonotope <-> max(A@x-b)>=0 (you might wanna use 1e-6 as a threshold instead for numerical stability)

A point, x, is inside of a zonotope <-> max(A@x-b)<0

project(dim=[0, 1])

The projection of a zonotope onto the specified dimensions self: <zonotope> dim: <int> or <list> or <torch.Tensor> dimensions for prjection

return <zonotope>

reduce(order, option='girard')

property shape

The shape of vector elements (ex. center) of a zonotope return <tuple>, (nx,)

slice(slice_dim, slice_pt)

slice zonotope on specified point in a certain dimension self: <zonotope> slice_dim: <torch.Tensor> or <list> or <int> , shape [] slice_pt: <torch.Tensor> or <list> or <float> or <int> , shape [] return <zonotope>

to(dtype=None, device=None)

Change the device and data type of a zonotope dtype: torch.float or torch.double device: ‘cpu’, ‘gpu’, ‘cuda:0’, …

to_interval()

Convert zonotope to interval return <interval>

to_polyZonotope(dim=None, id=None)

Convert zonotope to polynomial zonotope self: <zonotope> dim: <int>, dimension to take as sliceable return <polyZonotope>