zonopy.matPolyZonotope

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

Bases: object

2D Matrix Polynomial Zonotopes

The matrix polynomial zonotope is analogous to the polynomial zonotope like the matrix zonotope is to the zonotope.

It is defined as a set of the following form:

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

where

• $C\in\mathbb{R}^{dx\times dy}$ is the center matrix,

• $\mathbf{G}_{(i)}\in\mathbb{R}^{dx\times dy}$ is a single dependent generator, with $\mathbf{G} = [\mathbf{G}_{(1)},...,\mathbf{G}_{(N)}]$,

• $\mathbf{G}_{rest(j))}\in\mathbb{R}^{dx\times dy}$ is a single independent generator, with $\mathbf{G}_{rest} = [\mathbf{G}_{rest(1)},...,\mathbf{G}_{rest(M)}]$,

• $E\in\mathbb{R}^{p\times N}$ 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 matrix polynomial zonotope

Parameters:

• Z (torch.Tensor) – The center and generator tensor of the matrix polynomial zonotope $\mathbf{Z} = [C, \mathbf{G}_{(1)}, \ldots, \mathbf{G}_{(N)}, \mathbf{G}_{rest(1)}, \ldots, \mathbf{G}_{rest(M)}]$

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

• expMat (torch.Tensor, optional) – The exponent matrix. Default: None

• id (np.ndarray, optional) – The id array. Default: None

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

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

• device (torch.device, optional) – The device of the matrix 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 matrix polynomial zonotope
compress(compression_level)
cpu()
eye(dim[, dtype, device])
ones(dim1[, dim2, dtype, device])
reduce(order[, option])
reduce_indep(order[, option])
to([dtype, itype, device])
to_matZonotope()
zeros(dim1[, dim2, dtype, device])

Attributes

C
G
Grest
T
device
dtype
input_pairs
itype
n_cols
n_generators
n_indep_gens
n_rows
shape

property C

property G

property Grest

property T

compress(compression_level)

cpu()

property device

property dtype

static eye(dim, dtype=None, device=None)

property input_pairs

property itype

property n_cols

property n_generators

property n_indep_gens

property n_rows

static ones(dim1, dim2=None, dtype=None, device=None)

reduce(order, option='girard')

reduce_indep(order, option='girard')

property shape

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

to_matZonotope()

static zeros(dim1, dim2=None, dtype=None, device=None)