ZonoOpt Namespace Reference

Classes
class	Box
	Box (i.e., interval vector) class. More...
class	ConZono
	Constrained zonotope class. More...
class	EmptySet
	Empty Set class. More...
struct	ExternalSolverResults
	Abstract base for external-solver-specific solution metadata. More...
struct	GurobiSettings
	Settings for the dynamically-loaded Gurobi solver backend. More...
struct	GurobiSolverResults
	Solver-native solution metadata produced by the Gurobi backend. More...
class	HybZono
	Hybrid zonotope class. More...
class	Interval
	Interval class. More...
class	IntervalMatrix
	Class for interval matrices (i.e., every element of the matrix is an interval) More...
class	MI_Box
	Mixed-integer box. More...
struct	OptSettings
	Settings for the internal ZonoOpt ADMM / branch-and-bound solver. More...
struct	OptSolution
	Solution data structure for optimization routines in ZonoOpt library. More...
class	Point
	Point class. More...
struct	SCIPSettings
	Settings for the dynamically-loaded SCIP solver backend. More...
struct	SCIPSolverResults
	Solver-native solution metadata produced by the SCIP backend. More...
struct	SolverSettings
	Abstract base for all solver settings. More...
struct	WarmStartParams
	Warm start parameters for optimization routines in ZonoOpt library. More...
class	Zono
	Zonotope class. More...

Typedefs
using	json = nlohmann::json
typedef std::unique_ptr< HybZono >	ZonoPtr
	Type alias for a unique pointer to a (polymorphic) HybZono object. <>

Functions
std::unique_ptr< HybZono >	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 >	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 >	cartesian_product (const HybZono &Z1, HybZono &Z2)
	Computes the Cartesian product of two sets Z1 and Z2.
std::unique_ptr< HybZono >	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< ConZono >	convex_hull (const std::vector< std::shared_ptr< HybZono > > &Zs, bool exact=true)
	Computes convex hull of several sets.
std::unique_ptr< HybZono >	from_json (const std::string &filename)
	Read a HybZono object from a JSON file.
const SolverSettings &	get_default_solver_settings ()
	Returns a reference to the current program-wide default solver settings.
std::unique_ptr< HybZono >	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 >	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 >	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< Zono >	interval_2_zono (const Box &box)
	Builds a zonotope from a Box object.
std::unique_ptr< Zono >	make_regular_zono_2D (zono_float radius, int n_sides, bool outer_approx=false, const Eigen::Vector< zono_float, 2 > &c=Eigen::Vector< zono_float, 2 >::Zero())
	Builds a 2D regular zonotope with a given radius and number of sides.
std::unique_ptr< HybZono >	minkowski_sum (const HybZono &Z1, HybZono &Z2)
	Computes Minkowski sum of two sets Z1 and Z2.
std::unique_ptr< HybZono >	operator* (const Box &box, HybZono &Z)
Box	operator* (const Eigen::Matrix< zono_float, -1, -1 > &A, const Box &box)
IntervalMatrix	operator* (const Eigen::Matrix< zono_float, -1, -1 > &A, const IntervalMatrix &B)
std::unique_ptr< HybZono >	operator* (const Eigen::Matrix< zono_float, -1, -1 > &R, const HybZono &Z)
std::unique_ptr< HybZono >	operator* (const Eigen::SparseMatrix< zono_float > &R, const HybZono &Z)
Box	operator* (const Eigen::SparseMatrix< zono_float, Eigen::RowMajor > &A, const Box &box)
IntervalMatrix	operator* (const Eigen::SparseMatrix< zono_float, Eigen::RowMajor > &A, const IntervalMatrix &B)
Box	operator* (const Eigen::Vector< zono_float, -1 > &v, const Box &box)
Box	operator* (const Interval &interval, const Box &box)
IntervalMatrix	operator* (const Interval &interval, const IntervalMatrix &A)
std::unique_ptr< HybZono >	operator* (const IntervalMatrix &R, const HybZono &Z)
Interval	operator* (const zono_float alpha, const Interval &interval)
Box	operator* (zono_float alpha, const Box &box)
IntervalMatrix	operator* (zono_float alpha, const IntervalMatrix &A)
std::unique_ptr< HybZono >	operator* (zono_float f, const HybZono &Z)
std::unique_ptr< HybZono >	operator+ (const Box &box, HybZono &Z)
Box	operator+ (const Eigen::Vector< zono_float, -1 > &v, const Box &box)
std::unique_ptr< HybZono >	operator+ (const Eigen::Vector< zono_float, -1 > &v, HybZono &Z)
IntervalMatrix	operator+ (const Interval &interval, const IntervalMatrix &mat)
Interval	operator+ (const zono_float alpha, const Interval &interval)
IntervalMatrix	operator+ (zono_float alpha, const IntervalMatrix &A)
Box	operator- (const Eigen::Vector< zono_float, -1 > &v, const Box &box)
IntervalMatrix	operator- (const Interval &interval, const IntervalMatrix &mat)
Interval	operator- (const zono_float alpha, const Interval &interval)
IntervalMatrix	operator- (zono_float alpha, const IntervalMatrix &A)
Box	operator/ (const Interval &interval, const Box &box)
IntervalMatrix	operator/ (const Interval &interval, const IntervalMatrix &A)
Interval	operator/ (const zono_float alpha, const Interval &interval)
Box	operator/ (zono_float alpha, const Box &box)
IntervalMatrix	operator/ (zono_float alpha, const IntervalMatrix &A)
std::ostream &	operator<< (std::ostream &os, const Box &box)
std::ostream &	operator<< (std::ostream &os, const HybZono &Z)
std::ostream &	operator<< (std::ostream &os, const Interval &interval)
std::ostream &	operator<< (std::ostream &os, const IntervalMatrix &interval_matrix)
int	perturb_binaries (const MI_Box &x_box, const Eigen::Ref< const Eigen::Vector< zono_float, -1 > > xk, Eigen::Ref< Eigen::Vector< zono_float, -1 > > zk, const bool restart, std::mt19937 &rand_gen)
std::unique_ptr< HybZono >	pontry_diff (HybZono &Z1, Zono &Z2, bool exact=true)
	Computes the Pontryagin difference Z1 - Z2.
std::unique_ptr< HybZono >	project_onto_dims (const HybZono &Z, const std::vector< int > &dims)
	Projects set Z onto the dimensions specified in dims.
void	set_default_solver_settings (const SolverSettings &settings)
	Replaces the program-wide default solver settings with a polymorphic copy of settings.
std::unique_ptr< HybZono >	set_diff (const HybZono &Z1, HybZono &Z2, zono_float delta_m=100, bool remove_redundancy=true, const SolverSettings &settings=get_default_solver_settings(), std::shared_ptr< OptSolution > *solution=nullptr, int n_leaves=std::numeric_limits< int >::max(), int contractor_iter=10)
	Set difference Z1 \ Z2.
void	to_json (const HybZono &Z, const std::string &filename)
	Write a HybZono object to a JSON file.
std::unique_ptr< HybZono >	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 >	vrep_2_conzono (const Eigen::Matrix< zono_float, -1, -1 > &Vpoly)
	Builds a constrained zonotope from a vertex representation polytope.
std::unique_ptr< HybZono >	vrep_2_hybzono (const std::vector< Eigen::Matrix< zono_float, -1, -1 > > &Vpolys, bool expose_indicators=false)
	Computes a hybrid zonotope from a union of vertex representation polytopes.
std::unique_ptr< HybZono >	zono_union_2_hybzono (std::vector< std::shared_ptr< Zono > > &Zs, bool expose_indicators=false)
	Computes a hybrid zonotope from a union of zonotopes.

Typedef Documentation

json

using ZonoOpt::json = typedef nlohmann::json

Function Documentation

get_default_solver_settings()

const SolverSettings & ZonoOpt::get_default_solver_settings ( )

inline

Returns a reference to the current program-wide default solver settings.

The returned reference is valid until the next call to set_default_solver_settings().

operator*() [1/15]

std::unique_ptr< HybZono > ZonoOpt::operator*	(	const Box &	box,
		HybZono &	Z
	)

Parameters

box
Z

Returns

std::unique_ptr<HybZono>

operator*() [2/15]

Box ZonoOpt::operator*	(	const Eigen::Matrix< zono_float, -1, -1 > &	A,
		const Box &	box
	)

Parameters

A	matrix to multiply

Returns

enclosure of A * this

operator*() [3/15]

IntervalMatrix ZonoOpt::operator*	(	const Eigen::Matrix< zono_float, -1, -1 > &	A,
		const IntervalMatrix &	B
	)

Parameters

A	lhs matrix
B	rhs interval matrix

Returns

resulting interval matrix

Exceptions

std::invalid_argument

if A's column count does not match B's row count.

operator*() [4/15]

std::unique_ptr< HybZono > ZonoOpt::operator*	(	const Eigen::Matrix< zono_float, -1, -1 > &	R,
		const HybZono &	Z
	)

Parameters

R
Z

Returns

std::unique_ptr<HybZono>

Exceptions

std::invalid_argument

if R's column count does not match Z's dimension.

operator*() [5/15]

std::unique_ptr< HybZono > ZonoOpt::operator*	(	const Eigen::SparseMatrix< zono_float > &	R,
		const HybZono &	Z
	)

Parameters

R
Z

Returns

std::unique_ptr<HybZono>

Exceptions

std::invalid_argument

if R's column count does not match Z's dimension.

operator*() [6/15]

Box ZonoOpt::operator*	(	const Eigen::SparseMatrix< zono_float, Eigen::RowMajor > &	A,
		const Box &	box
	)

Parameters

A	matrix to multiply

Returns

enclosure of A * this

operator*() [7/15]

IntervalMatrix ZonoOpt::operator*	(	const Eigen::SparseMatrix< zono_float, Eigen::RowMajor > &	A,
		const IntervalMatrix &	B
	)

Parameters

A	lhs matrix
B	rhs interval matrix

Returns

resulting interval matrix

Exceptions

std::invalid_argument

if A's column count does not match B's row count.

operator*() [8/15]

Box ZonoOpt::operator*	(	const Eigen::Vector< zono_float, -1 > &	v,
		const Box &	box
	)

Parameters

v	vector to multiply
box	box to multiply

Returns

enclosure of v * box (elementwise)

Exceptions

std::invalid_argument

if v does not have the same size as the Box.

operator*() [9/15]

Box ZonoOpt::operator*	(	const Interval &	interval,
		const Box &	box
	)

Parameters

interval	interval to multiply
box	box to multiply

Returns

enclosure of interval * box (elementwise)

operator*() [10/15]

IntervalMatrix ZonoOpt::operator*	(	const Interval &	interval,
		const IntervalMatrix &	A
	)

Parameters

interval	interval to multiply
A	interval matrix

Returns

resulting interval matrix

operator*() [11/15]

std::unique_ptr< HybZono > ZonoOpt::operator*	(	const IntervalMatrix &	R,
		const HybZono &	Z
	)

Parameters

R
Z

Returns

std::unique_ptr<HybZono>

Exceptions

std::invalid_argument

if R's column count does not match Z's dimension.

operator*() [12/15]

Interval ZonoOpt::operator*	(	const zono_float	alpha,
		const Interval &	interval
	)

Parameters

alpha	scalar
interval	interval

Returns

enclosure of alpha * interval

operator*() [13/15]

Box ZonoOpt::operator*	(	zono_float	alpha,
		const Box &	box
	)

Parameters

alpha	scalar multiplier
box	box to multiply

Returns

enclosure of alpha * box (elementwise)

operator*() [14/15]

IntervalMatrix ZonoOpt::operator*	(	zono_float	alpha,
		const IntervalMatrix &	A
	)

Parameters

alpha	scalar multiplier
A	interval matrix

Returns

resulting interval matrix

operator*() [15/15]

std::unique_ptr< HybZono > ZonoOpt::operator*	(	zono_float	f,
		const HybZono &	Z
	)

Parameters

f
Z

Returns

std::unique_ptr<HybZono>

operator+() [1/6]

std::unique_ptr< HybZono > ZonoOpt::operator+	(	const Box &	box,
		HybZono &	Z
	)

Parameters

box
Z

Returns

std::unique_ptr<HybZono>

Exceptions

std::invalid_argument

if box does not have the same dimension as Z.

operator+() [2/6]

Box ZonoOpt::operator+	(	const Eigen::Vector< zono_float, -1 > &	v,
		const Box &	box
	)

Parameters

v	vector to add
box	box to add

Returns

enclosure of v + box (elementwise)

Exceptions

std::invalid_argument

if v does not have the same size as the Box.

operator+() [3/6]

std::unique_ptr< HybZono > ZonoOpt::operator+	(	const Eigen::Vector< zono_float, -1 > &	v,
		HybZono &	Z
	)

Parameters

v
Z

Returns

std::unique_ptr<HybZono>

Exceptions

std::invalid_argument

if v does not have the same dimension as Z.

operator+() [4/6]

IntervalMatrix ZonoOpt::operator+	(	const Interval &	interval,
		const IntervalMatrix &	mat
	)

Parameters

interval	interval to add
mat	interval matrix

Returns

resulting interval matrix

operator+() [5/6]

Interval ZonoOpt::operator+	(	const zono_float	alpha,
		const Interval &	interval
	)

Parameters

alpha	scalar
interval	interval

Returns

enclosure of alpha + interval

operator+() [6/6]

IntervalMatrix ZonoOpt::operator+	(	zono_float	alpha,
		const IntervalMatrix &	A
	)

Parameters

alpha	scalar to add
A	interval matrix

Returns

resulting interval matrix

operator-() [1/4]

Box ZonoOpt::operator-	(	const Eigen::Vector< zono_float, -1 > &	v,
		const Box &	box
	)

Parameters

v	vector
box	box to subtract

Returns

enclosure of v - box (elementwise)

Exceptions

std::invalid_argument

if v does not have the same size as the Box.

operator-() [2/4]

IntervalMatrix ZonoOpt::operator-	(	const Interval &	interval,
		const IntervalMatrix &	mat
	)

Parameters

interval	interval
mat	interval matrix to subtract

Returns

resulting interval matrix

operator-() [3/4]

Interval ZonoOpt::operator-	(	const zono_float	alpha,
		const Interval &	interval
	)

Parameters

alpha	scalar
interval	interval

Returns

enclosure of alpha - interval

operator-() [4/4]

IntervalMatrix ZonoOpt::operator-	(	zono_float	alpha,
		const IntervalMatrix &	A
	)

Parameters

alpha	scalar
A	interval matrix to subtract

Returns

resulting interval matrix

operator/() [1/5]

Box ZonoOpt::operator/	(	const Interval &	interval,
		const Box &	box
	)

Parameters

interval	interval
box	box to divide

Returns

enclosure of interval / box (elementwise)

operator/() [2/5]

IntervalMatrix ZonoOpt::operator/	(	const Interval &	interval,
		const IntervalMatrix &	A
	)

Parameters

interval	interval
A	matrix to divide

Returns

resulting interval matrix (interval / this)

operator/() [3/5]

Interval ZonoOpt::operator/	(	const zono_float	alpha,
		const Interval &	interval
	)

Parameters

alpha	scalar
interval	interval

Returns

enclosure of alpha / interval

operator/() [4/5]

Box ZonoOpt::operator/	(	zono_float	alpha,
		const Box &	box
	)

Parameters

alpha	scalar divisor
box	box to divide

Returns

enclosure of alpha / box (elementwise)

operator/() [5/5]

IntervalMatrix ZonoOpt::operator/	(	zono_float	alpha,
		const IntervalMatrix &	A
	)

Parameters

alpha	scalar
A	matrix to divide

Returns

resulting interval matrix (alpha / this)

operator<<() [1/4]

std::ostream & ZonoOpt::operator<<	(	std::ostream &	os,
		const Box &	box
	)

Parameters

os	ostream
box	reference to box

Returns

ostream

operator<<() [2/4]

std::ostream & ZonoOpt::operator<<	(	std::ostream &	os,
		const HybZono &	Z
	)

Parameters

os
Z

operator<<() [3/4]

std::ostream & ZonoOpt::operator<<	(	std::ostream &	os,
		const Interval &	interval
	)

Parameters

os
interval

Returns

ostream reference

operator<<() [4/4]

std::ostream & ZonoOpt::operator<<	(	std::ostream &	os,
		const IntervalMatrix &	interval_matrix
	)

Parameters

os	ostream
interval_matrix	reference to interval matrix

Returns

ostream

perturb_binaries()

int ZonoOpt::perturb_binaries	(	const MI_Box &	x_box,
		const Eigen::Ref< const Eigen::Vector< zono_float, -1 > >	xk,
		Eigen::Ref< Eigen::Vector< zono_float, -1 > >	zk,
		const bool	restart,
		std::mt19937 &	rand_gen
	)

set_default_solver_settings()

void ZonoOpt::set_default_solver_settings ( const SolverSettings &  settings )

inline

Replaces the program-wide default solver settings with a polymorphic copy of settings.

After this call, any ZonoOpt optimization method invoked without an explicit settings argument will use a freshly resolved reference to the new default.

Exceptions

std::runtime_error

if the backend selected by settings cannot be initialized (e.g., a GurobiSettings whose Gurobi library cannot be dynamically loaded). The existing default is left unchanged on throw.