Functions

The functionality provided in zonoLab is organized into five categories: properties, arithmetic, visualization, complexity, and auxiliary. The following provides a brief discussion of each function. More detailed information for using each function is available in the comments at the top of each file.

Properties

• Get leaves - getLeaves - returns all combinations of binary factors that result in non empty sets. Note: requires Gurobi.

Arithmetic

• Generalized intersection - and or & - computes the generalized intersection of two sets with an optional third argument for a matrix.

• Bounding box - boundingBox - computes the axis-aligned bounding-box of a set and returns a zonotope with a diagonal generator matrix.

• Cartesian product - cartProd - computes the Cartesian product of two sets.

• Convex hull - convexHull - computes the convex hull of two sets. Note: currently, only available for zonotopes and constrained zonotopes.

• Halfspace intersection - halfspaceIntersection - computes the intersection of a set with one or more halfspaces. Can also be used to compute the generalized halfspace intersection if a matrix is provided.

• Linear mapping - mtimes or * - computes the linear mapping of a set by a matrix or scalar.

• Minkowski sum - plus or + - computes the Minkowski sum of two sets.

• Pontryagin difference - pontryDiff - computes the Pontryagin difference of two sets. Note: currently, the subtrahend must be a zonotope.

• ReLU Neural Network - reluNN - computes the set-based mapping of a multi-layer ReLU-based neural network based on user-provided weights and biases assuming a bounded domain for each activation function.

• One-step MLD reachable set - stepMLD - computes the one-step reachable set of a Mixed-Logical-Dynamical (MLD) system.

• Support function - supportFunc - computes the value of the support function for a given set and one or more directions.

• Union - union - computes the union of two sets.

Visualization

• Plot - plot - plots a set with options to change the appearance of the set and to output the vertices and faces.

• Projection - projection - projects a set onto a subset of dimensions provided as a vector of indicies.

Complexity

• Methods to produce an inner- or outer-approximation of a set or an exact copy of a set with reduced set representation complexity are currently under development.

Auxiliary

• Match set type - matchSetType - returns sets of the same type for two input sets of differing types.

• Simplify set type - simplifySetType - returns the simpliest zonotopic set representation with zonotopes being more simple than constrained zonotopes and constrained zonotopes more simple than hybrid zonotopes.