Set Operations

Set operations for ZonoOpt library. More...

Functions
std::unique_ptr< HybZono >	ZonoOpt::affine_map (const HybZono &Z, const Eigen::SparseMatrix< zono_float > &R, const Eigen::Vector< zono_float, -1 > &s=Eigen::Vector< zono_float, -1 >())
	Returns affine map R*Z + s of set Z.
std::unique_ptr< HybZono >	ZonoOpt::affine_inclusion (const HybZono &Z, const IntervalMatrix &R, const Eigen::Vector< zono_float, -1 > &s=Eigen::Vector< zono_float, -1 >())
	Returns inclusion of zonotopic set for uncertain affine map R*Z + s.
std::unique_ptr< HybZono >	ZonoOpt::project_onto_dims (const HybZono &Z, const std::vector< int > &dims)
	Projects set Z onto the dimensions specified in dims.
std::unique_ptr< HybZono >	ZonoOpt::minkowski_sum (const HybZono &Z1, HybZono &Z2)
	Computes Minkowski sum of two sets Z1 and Z2.
std::unique_ptr< HybZono >	ZonoOpt::pontry_diff (HybZono &Z1, Zono &Z2, bool exact=true)
	Computes the Pontryagin difference Z1 - Z2.
std::unique_ptr< HybZono >	ZonoOpt::intersection (const HybZono &Z1, HybZono &Z2, const Eigen::SparseMatrix< zono_float > &R=Eigen::SparseMatrix< zono_float >())
	Computes the generalized intersection of sets Z1 and Z2 over the matrix R.
std::unique_ptr< HybZono >	ZonoOpt::intersection_over_dims (const HybZono &Z1, HybZono &Z2, const std::vector< int > &dims)
	Computes the generalized intersection of sets Z1 and Z2 over the specified dimensions.
std::unique_ptr< HybZono >	ZonoOpt::halfspace_intersection (HybZono &Z, const Eigen::SparseMatrix< zono_float > &H, const Eigen::Vector< zono_float, -1 > &f, const Eigen::SparseMatrix< zono_float > &R=Eigen::SparseMatrix< zono_float >())
	Computes the intersection generalized intersection of set Z with halfspace H*x <= f over matrix R.
std::unique_ptr< HybZono >	ZonoOpt::union_of_many (const std::vector< std::shared_ptr< HybZono > > &Zs, bool preserve_sharpness=false, bool expose_indicators=false)
	Computes union of several sets.
std::unique_ptr< ConZono >	ZonoOpt::convex_hull (const std::vector< std::shared_ptr< HybZono > > &Zs)
	Computes convex hull of several sets.
std::unique_ptr< HybZono >	ZonoOpt::cartesian_product (const HybZono &Z1, HybZono &Z2)
	Computes the Cartesian product of two sets Z1 and Z2.
std::unique_ptr< HybZono >	ZonoOpt::constrain (HybZono &Z, const Eigen::SparseMatrix< zono_float > &H, const Eigen::Vector< zono_float, -1 > &f, char direction, const Eigen::SparseMatrix< zono_float > &R=Eigen::SparseMatrix< zono_float >())
	Computes the generalized intersection of set Z with H*x <= f, H*x >= f, or H*x = f over matrix R.
std::unique_ptr< HybZono >	ZonoOpt::set_diff (const HybZono &Z1, HybZono &Z2, zono_float delta_m=100, bool remove_redundancy=true, const OptSettings &settings=OptSettings(), std::shared_ptr< OptSolution > *solution=nullptr, int n_leaves=std::numeric_limits< int >::max(), int contractor_iter=10)
	Set difference Z1 \ Z2.

Detailed Description

Set operations for ZonoOpt library.

Function Documentation

affine_inclusion()

std::unique_ptr< HybZono > ZonoOpt::affine_inclusion	(	const HybZono &	Z,
		const IntervalMatrix &	R,
		const Eigen::Vector< zono_float, -1 > &	s = Eigen::Vector<zono_float, -1>()
	)

Returns inclusion of zonotopic set for uncertain affine map R*Z + s.

Parameters

Z	zonotopic set
R	interval matrix
s	vector offset

Returns

zonotopic set

This computes an over-approximation of the affine map using the method of Rego et. al. (2020) "Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems" The SVD-based zonotope over-approximation method is used in this function when Z is a constrained zonotope. When Z is a hybrid zonotope, the convex relaxation is used to produce a constrained zonotope, and then the SVD-based method is applied.

affine_map()

std::unique_ptr< HybZono > ZonoOpt::affine_map	(	const HybZono &	Z,
		const Eigen::SparseMatrix< zono_float > &	R,
		const Eigen::Vector< zono_float, -1 > &	s = Eigen::Vector<zono_float, -1>()
	)

Returns affine map R*Z + s of set Z.

Parameters

Z	zonotopic set
R	affine map matrix
s	vector offset

Returns

zonotopic set

cartesian_product()

std::unique_ptr< HybZono > ZonoOpt::cartesian_product	(	const HybZono &	Z1,
		HybZono &	Z2
	)

Computes the Cartesian product of two sets Z1 and Z2.

Parameters

Z1	zonotopic set
Z2	zonotopic set

Returns

zonotopic set

constrain()

std::unique_ptr< HybZono > ZonoOpt::constrain	(	HybZono &	Z,
		const Eigen::SparseMatrix< zono_float > &	H,
		const Eigen::Vector< zono_float, -1 > &	f,
		char	direction,
		const Eigen::SparseMatrix< zono_float > &	R = Eigen::SparseMatrix<zono_float>()
	)

Computes the generalized intersection of set Z with H*x <= f, H*x >= f, or H*x = f over matrix R.

Parameters

Z	zonotopic set
H	constraint matrix
f	constraint vector
direction	'<' for <=, '>' for >=, '=' for =
R	affine map matrix, defaults to identity

Returns

zonotopic set

convex_hull()

std::unique_ptr< ConZono > ZonoOpt::convex_hull

(

const std::vector< std::shared_ptr< HybZono > > &

Zs

)

Computes convex hull of several sets.

Parameters

Zs	Sets for which convex hull is to be computed.

Returns

constrained zonotope convex hull

Computes convex hull of sets {Z0, Z1, ..., Zn}. If Zi is a hybrid zonotope, it must be sharp or this function will throw an error.

halfspace_intersection()

std::unique_ptr< HybZono > ZonoOpt::halfspace_intersection	(	HybZono &	Z,
		const Eigen::SparseMatrix< zono_float > &	H,
		const Eigen::Vector< zono_float, -1 > &	f,
		const Eigen::SparseMatrix< zono_float > &	R = Eigen::SparseMatrix<zono_float>()
	)

Computes the intersection generalized intersection of set Z with halfspace H*x <= f over matrix R.

Parameters

Z	zonotopic set
H	halfspace matrix
f	halfspace vector
R	affine map matrix

Returns

zonotopic set

Calls constrain with '<'

intersection()

std::unique_ptr< HybZono > ZonoOpt::intersection	(	const HybZono &	Z1,
		HybZono &	Z2,
		const Eigen::SparseMatrix< zono_float > &	R = Eigen::SparseMatrix<zono_float>()
	)

Computes the generalized intersection of sets Z1 and Z2 over the matrix R.

Parameters

Z1	zonotopic set
Z2	zonotopic set
R	affine map matrix

Returns

zonotopic set

intersection_over_dims()

std::unique_ptr< HybZono > ZonoOpt::intersection_over_dims	(	const HybZono &	Z1,
		HybZono &	Z2,
		const std::vector< int > &	dims
	)

Computes the generalized intersection of sets Z1 and Z2 over the specified dimensions.

Parameters

Z1	zonotopic set
Z2	zonotopic set
dims	vector of dimensions

Returns

zonotopic set

minkowski_sum()

std::unique_ptr< HybZono > ZonoOpt::minkowski_sum	(	const HybZono &	Z1,
		HybZono &	Z2
	)

Computes Minkowski sum of two sets Z1 and Z2.

Parameters

Z1	zonotopic set
Z2	zonotopic set

Returns

zonotopic set

pontry_diff()

std::unique_ptr< HybZono > ZonoOpt::pontry_diff	(	HybZono &	Z1,
		Zono &	Z2,
		bool	exact = true
	)

Computes the Pontryagin difference Z1 - Z2.

Parameters

Z1	minuend
Z2	subtrahend
exact	require output to be exact, otherwise inner approximation will be returned (default true)

Returns

zonotopic set

For inner approximations (exact = false), the algorithm from Vinod et. al. 2025 is used. Note that this algorithm is exact when the minuend is a constrained zonotope and the matrix [G;A] is invertible. Exact Pontryagin difference can only be computed when the subtrahend is a zonotope.

project_onto_dims()

std::unique_ptr< HybZono > ZonoOpt::project_onto_dims	(	const HybZono &	Z,
		const std::vector< int > &	dims
	)

Projects set Z onto the dimensions specified in dims.

Parameters

Z	zonotopic set
dims	vector of dimensions

Returns

zonotopic set

set_diff()

std::unique_ptr< HybZono > ZonoOpt::set_diff	(	const HybZono &	Z1,
		HybZono &	Z2,
		zono_float	delta_m = 100,
		bool	remove_redundancy = true,
		const OptSettings &	settings = OptSettings(),
		std::shared_ptr< OptSolution > *	solution = nullptr,
		int	n_leaves = std::numeric_limits<int>::max(),
		int	contractor_iter = 10
	)

Set difference Z1 \ Z2.

Parameters

Z1	zonotopic set
Z2	zonotopic set
delta_m	parameter defining range of complement
remove_redundancy	remove redundant constraints and unused generators in get_leaves function call
settings	optimization settings for get_leaves function call
solution	optimization solution for get_leaves function call
n_leaves	maximum number of leaves to return in get_leaves function call
contractor_iter	number of interval contractor iterations to run if using remove_redundancy

Returns

zonotopic set

union_of_many()

std::unique_ptr< HybZono > ZonoOpt::union_of_many	(	const std::vector< std::shared_ptr< HybZono > > &	Zs,
		bool	preserve_sharpness = false,
		bool	expose_indicators = false
	)

Computes union of several sets.

Parameters

Zs	Sets to be unioned.
preserve_sharpness	Flag to preserve sharpness of the union at expense of complexity.
expose_indicators	Flag to append indicator set to the union.

Returns

zonotopic set

Computes union of sets {Z0, Z1, ..., Zn}. If expose_indicators is true, returns union({Z0, ..., Zn}) x I where I is the indicator set for the union. Specifically, each dimension of I corresponds to one of the Zi in the union. So for union_of_many({Z0, Z1, Z2}, true) with Z0, Z1, Z2 not intersecting, if a vector [z, i] is in union({Z0, Z1, Z2}) x I, then i = [1, 0, 0] if z is in Z0, etc.