zonopy.interval

class zonopy.interval(inf=None, sup=None, dtype=None, device=None)

Bases: object

N-rank tensor intervals

An interval is a set of real numbers that includes all numbers between two given numbers. Here, we define an interval as a set of real numbers given infinum and supremum tensors $\underbar{X}$ and $\overline{\text{X}}$ such that $\underbar{X} \leq X \leq \overline{\text{X}}$.

$$\mathcal{I} := \left\{ x \in \mathbb{R}^{n,m,...} \; \middle\vert \; \begin{array}{c} \underbar{x}_{i,j,\ldots} \leq x_{i,j,\ldots} \leq \overline{\text{x}}_{i,j,\ldots} \\ \forall{i=1,\ldots,n} \\ \forall{j=1,\ldots,m} \\ \vdots \end{array} \right\}$$

__init__(inf=None, sup=None, dtype=None, device=None)

Create an interval

If inf and sup are both None, an empty interval is created. If only one of inf or sup is None, the interval is created as a point interval where inf = sup.

Parameters:

• inf (torch.Tensor, optional) – infimum of the interval. Defaults to None.

• sup (torch.Tensor, optional) – supremum of the interval. Defaults to None.

• dtype (torch.dtype, optional) – data type of the interval. If None, the data type is inferred from the input tensors. Defaults to None.

• device (torch.device, optional) – device of the interval. If None, the device is inferred from the input tensors. Defaults to None.

Raises:

• AssertionError – If the shapes of inf and sup do not match.

• AssertionError – If the devices of inf and sup do not match.

• AssertionError – If inf is not less than or equal to sup entry-wise and zonopy.internal.__debug_extra__ is True.

Methods

__init__([inf, sup, dtype, device])	Create an interval
center()	Compute the center of the interval
cpu()	Change the device of an interval to CPU
dim()	Returns the number of dimensions of the interval
numel()	Returns the total number of elements in the interval
rad()	Compute the radius of the interval
t()	Transposes the interval
to([dtype, device])	Change the device and data type of an interval dtype: torch.float or torch.double device: 'cpu', 'gpu', 'cuda:0', ...

Attributes

device	The device of an interval properties return 'cpu', 'cuda:0', or ...
dtype	The data type of an interval properties return torch.float or torch.double
inf	The infimum of an interval return <torch.Tensor> ,shape [n,m]
shape	The shape of elements (infimum or supremum) of an interval
sup	The supremum of an interval return <torch.Tensor> ,shape [n,m]

center() → torch.Tensor

Compute the center of the interval

The center of the interval is the midpoint of the infimum and supremum.

Returns:

center of the interval

Return type:

torch.Tensor

cpu()

Change the device of an interval to CPU

property device

The device of an interval properties return ‘cpu’, ‘cuda:0’, or …

dim() → int

Returns the number of dimensions of the interval

Returns:

number of dimensions of the interval

Return type:

int

property dtype

The data type of an interval properties return torch.float or torch.double

property inf

The infimum of an interval return <torch.Tensor> ,shape [n,m]

numel() → int

Returns the total number of elements in the interval

Returns:

number of elements in the interval

Return type:

int

rad() → torch.Tensor

Compute the radius of the interval

The radius of the interval is half of the difference between the supremum and infimum. It can be viewed as the distance from the center to the infimum or supremum.

Returns:

radius of the interval

Return type:

torch.Tensor

property shape

The shape of elements (infimum or supremum) of an interval

property sup

The supremum of an interval return <torch.Tensor> ,shape [n,m]

t()

Transposes the interval

Returns:

transposed interval

Return type:

interval

to(dtype=None, device=None)

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