Set Types¶

NNV’s set representations for reachability analysis. Each type captures a region of possible values with linear constraints on predicate variables.

Star¶

The fundamental polytopic set representation.

Constructors:

S = Star(lb, ub)                              % From box bounds
S = Star(V, C, d)                             % From basis matrix and constraints
S = Star(V, C, d, pred_lb, pred_ub)           % With predicate bounds

Key Properties: V (basis matrix), C, d (constraints), dim, nVar, predicate_lb, predicate_ub, state_lb, state_ub

Methods:

Method	Description
`S2 = S.affineMap(W, b)`	Apply affine transformation: y = Wx + b
`[lb, ub] = S.getRanges()`	Compute element-wise bounds via LP
`S2 = S.intersectHalfSpace(H, g)`	Intersect with half-space Hx <= g
`bool = S.contains(x)`	Check if point x is in the set
`bool = S.isEmptySet()`	Check if set is empty (infeasible constraints)
`S3 = S.MinkowskiSum(S2)`	Minkowski sum with another Star
`points = S.sample(N)`	Sample N random points from the set
`S.plot()`	Visualize the set (2D/3D projections)
`box = S.getBox()`	Get bounding box
`Z = S.getZono()`	Get zonotope outer approximation
`IS = S.toImageStar(h, w, c)`	Convert to ImageStar with given dimensions
`P = S.toPolyhedron()`	Convert to Polyhedron object

ImageStar¶

Star set for 2D multi-channel images (H x W x C).

Constructors:

IS = ImageStar(IM, LB, UB)            % From image + perturbation bounds
IS = ImageStar(lb_image, ub_image)     % From lower/upper bound images

Key Methods: Same as Star plus toStar(), estimateRanges()

Key Properties: height, width, numChannel, im_lb, im_ub

VolumeStar¶

Star set for 3D volumetric data (H x W x D x C).

Constructors:

VS = VolumeStar(VOL, LB, UB)          % From volume + perturbation bounds

Key Methods: Same interface as ImageStar, for 4D tensors.

Key Properties: height, width, depth, numChannel

GraphStar¶

Star set for graph node features (N x F).

Constructors:

GS = GraphStar(NF, LB, UB)            % Node features + perturbation bounds

Key Properties: V (3D: numNodes x numFeatures x numBasis), numNodes, numFeatures

Zono (Zonotope)¶

Centrally symmetric polytope defined by center and generators.

Constructor:

Z = Zono(c, V)    % c: center, V: generator matrix

Key Methods: affineMap, MinkowskiSum, getBox, toStar

Box¶

Axis-aligned hyper-rectangle.

Constructor:

B = Box(lb, ub)

Key Methods: toStar(), center, generators

HalfSpace¶

Linear constraint Gx <= g, used for safety specifications.

Constructor:

HS = HalfSpace(G, g)

Usage: Passed to verify_specification() to define the unsafe output region.