zonopy.polyZonotope

class zonopy.polyZonotope(Z, n_dep_gens=0, expMat=None, id=None, copy_Z=True, dtype=None, device=None)

Bases: object

1D Polynomial Zonotopes

The Polynomial Zonotope (similar to Talyor model) is a non-convex set representation of a summation over multivariate polynomials multiplied with intervals.

It is defined as a set of the following form:

$$\mathcal{PZ} := \left\{ c + \sum_{i=1}^{N} \left( \prod_{k=1}^{p}\alpha_{k}^{E_{(k,i)}}\right) G_{(\cdot,i)}+\sum_{j=1}^{M}\beta_{j}G_{rest(\cdot,j)} \; \middle\vert \; \begin{array}{l} \alpha_k, \beta_j \in [-1,1] \\ \forall k = 1,...,p \\ \forall j=1,...,M \end{array} \right\}$$

where

• $c\in\mathbb{R}^d$ is the center vector,

• $G\in\mathbb{R}^{d\times N}$ is the dependent generator matrix,

• $G_{rest}\in\mathbb{R}^{d\times M}$ is the independent generator matrix,

• $E\in\mathbb{R}^{p\times N}$ is the exponent matrix,

• $N$ is the number of dependent generators,

• $M$ is the number of independent generators, and

• $p$ is the number of indeterminants.

__init__(Z, n_dep_gens=0, expMat=None, id=None, copy_Z=True, dtype=None, device=None)

Initialize the polynomial zonotope

Parameters:

• Z (torch.Tensor) – The center and generator matrix of the polynomial zonotope $\mathbf{Z} = [c, G, G_{rest}]^T$

• n_dep_gens (int, optional) – The number of dependent generators. Default: 0

• expMat (torch.Tensor, optional) – The exponent matrix of the dependent generators. If None, it will be the identity matrix. Default: None

• id (torch.Tensor, optional) – The integer identifiers for the dependent generators. If None, it will be the range of the number of dependent generators. Default: None

• copy_Z (bool, optional) – If True, it will copy the input Z value. Default: True

• dtype (torch.dtype, optional) – The data type of the polynomial zonotope. If None, it will be inferred. Default: None

• device (torch.device, optional) – The device of the polynomial zonotope. If None, it will be inferred. Default: None

Raises:

• AssertionError – If the exponent matrix does not seem to be valid for the given dependent generators or ids.

• AssertionError – If the number of dependent generators does not match the number of ids.

• AssertionError – If the exponent matrix is not a non-negative integer matrix.

Methods

__init__(Z[, n_dep_gens, expMat, id, ...])	Initialize the polynomial zonotope
center_slice_all_dep(val_slc)
compress(compression_level)
cpu()
deleteZerosGenerators([eps])
exactCartProd(other)	self: <polyZonotope> other: <polyZonotope> return <polyZonotope>
grad_center_slice_all_dep(val_slc)
hess_center_slice_all_dep(val_slc)
ones(dims[, dtype, device])
project([dim])
reduce(order[, option])
reduce_indep(order[, option])
slice_all_dep(val_slc)	Slice polynomial zonotpe in all depdent generators
slice_dep(id_slc, val_slc)	Slice polynomial zonotpe in depdent generators id_slc: id to slice val_slc: indeterminant to slice
split_dep_indep([center_on_dep])
to([dtype, itype, device])
to_interval([method])
to_zonotope()
zeros(dims[, dtype, device])

Attributes

G	Dependent generators of a polynimal zonotope return <torch.Tensor> , shape [N, nx]
Grest	Independent generators of a polynimal zonotope return <torch.Tensor> , shape [M, nx]
c	The center of a polynimal zonotope return <torch.Tensor> , shape [nx]
device	The device of a polynomial zonotope properties return 'cpu', 'cuda:0', or ...
dimension
dtype	The data type of vector elements (ex.
input_pairs
itype	The data type of a polynomial zonotope exponent matrix return torch.short, torch.int, torch.long
n_generators
n_indep_gens

property G

Dependent generators of a polynimal zonotope return <torch.Tensor> , shape [N, nx]

property Grest

Independent generators of a polynimal zonotope return <torch.Tensor> , shape [M, nx]

property c

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

center_slice_all_dep(val_slc)

compress(compression_level)

cpu()

deleteZerosGenerators(eps=0)

property device

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

property dimension

property dtype

The data type of vector elements (ex. center) of a polynomial zonotope return torch.float or torch.double

exactCartProd(other)

self: <polyZonotope> other: <polyZonotope> return <polyZonotope>

grad_center_slice_all_dep(val_slc)

hess_center_slice_all_dep(val_slc)

property input_pairs

property itype

The data type of a polynomial zonotope exponent matrix return torch.short, torch.int, torch.long

property n_generators

property n_indep_gens

static ones(dims, dtype=None, device=None)

project(dim=[0, 1])

reduce(order, option='girard')

reduce_indep(order, option='girard')

slice_all_dep(val_slc)

Slice polynomial zonotpe in all depdent generators

id_slc: id to slice val_slc: indeterminant to slice return, c: <torch.Tensor>, shape [nx] grad_c: <torch.Tensor>, shape [n_ids,nx]

slice_dep(id_slc, val_slc)

Slice polynomial zonotpe in depdent generators id_slc: id to slice val_slc: indeterminant to slice

split_dep_indep(center_on_dep=True)

to(dtype=None, itype=None, device=None)

to_interval(method='interval')

to_zonotope()

static zeros(dims, dtype=None, device=None)