Zonotope class. More...

#include <Zono.hpp>

Inheritance diagram for ZonoOpt::Zono:

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Collaboration diagram for ZonoOpt::Zono:

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Public Member Functions
	Zono ()
	Default constructor for Zono class.

	Zono (const Eigen::SparseMatrix< zono_float > &G, const Eigen::Vector< zono_float, -1 > &c, const bool zero_one_form=false)
	Zono constructor.

	~Zono () override=default

void	set (const Eigen::SparseMatrix< zono_float > &G, const Eigen::Vector< zono_float, -1 > &c, bool zero_one_form=false)
	Reset zonotope object with the given parameters.

HybZono *	clone () const override
	Clone method for polymorphic behavior.

std::unique_ptr< Zono >	reduce_order (int n_o)
	Perform zonotope order reduction.

zono_float	get_volume ()
	Get volume of zonotope.

void	convert_form () override
	Converts the set representation between -1-1 and 0-1 forms.

std::string	print () const override
	Returns set information as a string.

Public Member Functions inherited from ZonoOpt::ConZono
	ConZono ()
	Default constructor for ConZono class.

	ConZono (const Eigen::SparseMatrix< zono_float > &G, const Eigen::Vector< zono_float, -1 > &c, const Eigen::SparseMatrix< zono_float > &A, const Eigen::Vector< zono_float, -1 > &b, bool zero_one_form=false)
	ConZono constructor.

	~ConZono () override=default

void	set (const Eigen::SparseMatrix< zono_float > &G, const Eigen::Vector< zono_float, -1 > &c, const Eigen::SparseMatrix< zono_float > &A, const Eigen::Vector< zono_float, -1 > &b, bool zero_one_form=false)
	Reset constrained zonotope object with the given parameters.

virtual void	constraint_reduction ()
	Execute constraint reduction algorithm from Scott et. al. 2016.

virtual std::unique_ptr< Zono >	to_zono_approx () const
	Compute outer approximation of constrained zonotope as zonotope using SVD.

Public Member Functions inherited from ZonoOpt::HybZono
	HybZono ()=default
	Default constructor for HybZono class.

	HybZono (const Eigen::SparseMatrix< zono_float > &Gc, const Eigen::SparseMatrix< zono_float > &Gb, const Eigen::Vector< zono_float, -1 > &c, const Eigen::SparseMatrix< zono_float > &Ac, const Eigen::SparseMatrix< zono_float > &Ab, const Eigen::Vector< zono_float, -1 > &b, bool zero_one_form=false, bool sharp=false)
	HybZono constructor.

virtual	~HybZono ()=default

void	set (const Eigen::SparseMatrix< zono_float > &Gc, const Eigen::SparseMatrix< zono_float > &Gb, const Eigen::Vector< zono_float, -1 > &c, const Eigen::SparseMatrix< zono_float > &Ac, const Eigen::SparseMatrix< zono_float > &Ab, const Eigen::Vector< zono_float, -1 > &b, bool zero_one_form=false, bool sharp=false)
	Reset hybrid zonotope object with the given parameters.

virtual int	get_n () const
	Returns dimension of set.

virtual int	get_nC () const
	Returns number of constraints in set definition.

virtual int	get_nG () const
	Returns number of generators in set definition.

virtual int	get_nGc () const
	Returns number of continuous generators in set definition.

virtual int	get_nGb () const
	Returns number of binary generators in set definition.

virtual Eigen::SparseMatrix< zono_float >	get_Gc () const
	Returns continuous generator matrix.

virtual Eigen::SparseMatrix< zono_float >	get_Gb () const
	Returns binary generator matrix.

virtual Eigen::SparseMatrix< zono_float >	get_G () const
	Returns generator matrix.

virtual Eigen::SparseMatrix< zono_float >	get_Ac () const
	Returns continuous constraint matrix.

virtual Eigen::SparseMatrix< zono_float >	get_Ab () const
	Returns binary constraint matrix.

virtual Eigen::SparseMatrix< zono_float >	get_A () const
	Returns constraint matrix.

virtual Eigen::Vector< zono_float, -1 >	get_c () const
	Returns center vector.

virtual Eigen::Vector< zono_float, -1 >	get_b () const
	Returns constraint vector.

virtual bool	is_0_1_form () const
	Returns true if factors are in range [0,1], false if they are in range [-1,1].

bool	is_sharp () const
	Returns true if set is known to be sharp.

virtual void	remove_redundancy (int contractor_iter=100)
	Removes redundant constraints and any unused generators.

virtual std::unique_ptr< ConZono >	convex_relaxation () const
	Returns convex relaxation of the hybrid zonotope.

virtual std::unique_ptr< HybZono >	complement (const zono_float delta_m=100, const bool remove_redundancy=true, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr, const int n_leaves=std::numeric_limits< int >::max(), const int contractor_iter=100)
	Computes the complement of the set Z.

bool	is_point () const
	Polymorphic type checking: true if set is a point.

bool	is_zono () const
	Polymorphic type checking: true if set is a zonotope.

bool	is_conzono () const
	Polymorphic type checking: true if set is a constrained zonotope.

bool	is_hybzono () const
	Polymorphic type checking: true if set is a hybrid zonotope.

bool	is_empty_set () const
	Polymorphic type checking: true if set is empty set object.

Eigen::Vector< zono_float, -1 >	optimize_over (const Eigen::SparseMatrix< zono_float > &P, const Eigen::Vector< zono_float, -1 > &q, zono_float c=0, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr) const
	Solves optimization problem with quadratic objective over the current set.

Eigen::Vector< zono_float, -1 >	project_point (const Eigen::Vector< zono_float, -1 > &x, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr) const
	Returns the projection of the point x onto the set object.

bool	is_empty (const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr) const
	Returns true if the set is provably empty, false otherwise.

zono_float	support (const Eigen::Vector< zono_float, -1 > &d, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr)
	Computes support function of the set in the direction d.

bool	contains_point (const Eigen::Vector< zono_float, -1 > &x, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr) const
	Checks whether the point x is contained in the set object.

Box	bounding_box (const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr)
	Computes a bounding box of the set object as a Box object.

std::vector< ConZono >	get_leaves (bool remove_redundancy=true, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr, int n_leaves=std::numeric_limits< int >::max(), int contractor_iter=10) const
	Computes individual constrained zonotopes whose union is the hybrid zonotope object.

Protected Member Functions
bool	do_is_empty (const OptSettings &, OptSolution *) const override

Box	do_bounding_box (const OptSettings &, OptSolution *) override

zono_float	do_support (const Eigen::Vector< zono_float, -1 > &d, const OptSettings &, OptSolution *) override

Protected Member Functions inherited from ZonoOpt::ConZono
OptSolution	qp_opt (const Eigen::SparseMatrix< zono_float > &P, const Eigen::Vector< zono_float, -1 > &q, zono_float c, const Eigen::SparseMatrix< zono_float > &A, const Eigen::Vector< zono_float, -1 > &b, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr) const

Eigen::Vector< zono_float, -1 >	do_optimize_over (const Eigen::SparseMatrix< zono_float > &P, const Eigen::Vector< zono_float, -1 > &q, zono_float c, const OptSettings &settings, OptSolution *solution) const override

Eigen::Vector< zono_float, -1 >	do_project_point (const Eigen::Vector< zono_float, -1 > &x, const OptSettings &settings, OptSolution *solution) const override

bool	do_contains_point (const Eigen::Vector< zono_float, -1 > &x, const OptSettings &settings, OptSolution *solution) const override

std::unique_ptr< HybZono >	do_complement (zono_float delta_m, bool, const OptSettings &, OptSolution *, int, int) override

Protected Member Functions inherited from ZonoOpt::HybZono
OptSolution	mi_opt (const Eigen::SparseMatrix< zono_float > &P, const Eigen::Vector< zono_float, -1 > &q, zono_float c, const Eigen::SparseMatrix< zono_float > &A, const Eigen::Vector< zono_float, -1 > &b, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr) const

std::vector< OptSolution >	mi_opt_multisol (const Eigen::SparseMatrix< zono_float > &P, const Eigen::Vector< zono_float, -1 > &q, zono_float c, const Eigen::SparseMatrix< zono_float > &A, const Eigen::Vector< zono_float, -1 > &b, int n_sols, const OptSettings &settings=OptSettings(), OptSolution *solution=nullptr) const

Additional Inherited Members
Static Protected Member Functions inherited from ZonoOpt::HybZono
static void	remove_generators (Eigen::SparseMatrix< zono_float > &G, Eigen::SparseMatrix< zono_float > &A, const std::set< int > &idx_to_remove)

static std::set< int >	find_unused_generators (const Eigen::SparseMatrix< zono_float > &G, const Eigen::SparseMatrix< zono_float > &A)

Protected Attributes inherited from ZonoOpt::HybZono
Eigen::SparseMatrix< zono_float >	G = Eigen::SparseMatrix<zono_float>(0, 0)
	generator matrix G = [Gc, Gb]

Eigen::SparseMatrix< zono_float >	Gc = Eigen::SparseMatrix<zono_float>(0, 0)
	continuous generator matrix

Eigen::SparseMatrix< zono_float >	Gb = Eigen::SparseMatrix<zono_float>(0, 0)
	binary generator matrix

Eigen::SparseMatrix< zono_float >	A = Eigen::SparseMatrix<zono_float>(0, 0)
	constraint matrix A = [Ac, Ab]

Eigen::SparseMatrix< zono_float >	Ac = Eigen::SparseMatrix<zono_float>(0, 0)
	continuous constraint matrix

Eigen::SparseMatrix< zono_float >	Ab = Eigen::SparseMatrix<zono_float>(0, 0)
	binary constraint matrix

Eigen::Vector< zono_float, -1 >	c = Eigen::Vector<zono_float, -1>(0)
	center vector

Eigen::Vector< zono_float, -1 >	b = Eigen::Vector<zono_float, -1>(0)
	constraint vector

int	n = 0
	set dimension

int	nG = 0
	total number of factors. nG = nGc + nGb

int	nGc = 0
	number of continuous factors

int	nGb = 0
	number of binary factors

int	nC = 0
	number of constraints

bool	zero_one_form = false
	flag to indicate whether the set is in 0-1 or -1-1 form

bool	sharp = false
	flag to indicate whether the set is known to be sharp (i.e., convex relaxation = convex hull)

Detailed Description

Zonotope class.

A zonotope is defined as: Z = {G * xi + c | xi in [-1, 1]^nG}. Equivalently, the following shorthand can be used: Z = <G, c>. Optionally, in 0-1 form, the factors are xi in [0, 1]^nG. The set dimension is n, and the number of equality constraints is nC.

Constructor & Destructor Documentation

◆ Zono() [1/2]

ZonoOpt::Zono::Zono ( )

inline

Default constructor for Zono class.

◆ Zono() [2/2]

ZonoOpt::Zono::Zono	(	const Eigen::SparseMatrix< zono_float > &	G,
		const Eigen::Vector< zono_float, -1 > &	c,
		const bool	zero_one_form = `false`
	)

Zono constructor.

Parameters

G	generator matrix
c	center
zero_one_form	true if set is in 0-1 form

◆ ~Zono()

ZonoOpt::Zono::~Zono ( )

overridedefault

Member Function Documentation

◆ clone()

HybZono * ZonoOpt::Zono::clone ( ) const

overridevirtual

Clone method for polymorphic behavior.

Reimplemented from ZonoOpt::ConZono.

◆ convert_form()

void ZonoOpt::Zono::convert_form ( )

overridevirtual

Converts the set representation between -1-1 and 0-1 forms.

This method converts the set representation between -1-1 and 0-1 forms. If the set is in -1-1 form, then xi_c in [-1,1] and xi_b in {-1,1}. If the set is in 0-1 form, then xi_c in [0,1] and xi_b in {0,1}.

Reimplemented from ZonoOpt::ConZono.

◆ do_bounding_box()

Box ZonoOpt::Zono::do_bounding_box	(	const OptSettings &	,
		OptSolution *
	)

overrideprotectedvirtual

Reimplemented from ZonoOpt::ConZono.

◆ do_is_empty()

bool ZonoOpt::Zono::do_is_empty	(	const OptSettings &	,
		OptSolution *
	)		const

overrideprotectedvirtual

Reimplemented from ZonoOpt::ConZono.

◆ do_support()

zono_float ZonoOpt::Zono::do_support	(	const Eigen::Vector< zono_float, -1 > &	d,
		const OptSettings &	,
		OptSolution *
	)

overrideprotectedvirtual

Reimplemented from ZonoOpt::ConZono.

◆ get_volume()

zono_float ZonoOpt::Zono::get_volume ( )

Get volume of zonotope.

Returns: volume

Reference: Gover and Krikorian 2010, "Determinants and the volumes of parallelotopes and zonotopes" Requires nG choose n determinant computations.

◆ print()

std::string ZonoOpt::Zono::print ( ) const

overridevirtual

Returns set information as a string.

Reimplemented from ZonoOpt::ConZono.

◆ reduce_order()

std::unique_ptr< Zono > ZonoOpt::Zono::reduce_order ( int n_o )

Perform zonotope order reduction.

Parameters

n_o	desired order, must be greater than or equal to the dimension of the set

Returns: zonotope with order n_o

◆ set()

void ZonoOpt::Zono::set	(	const Eigen::SparseMatrix< zono_float > &	G,
		const Eigen::Vector< zono_float, -1 > &	c,
		bool	zero_one_form = `false`
	)

Reset zonotope object with the given parameters.

Parameters

G	generator matrix
c	center
zero_one_form	true if set is in 0-1 form

The documentation for this class was generated from the following files:

/home/joshr/Documents/Projects/ZonoOpt/include/zonoopt/Zono.hpp
/home/joshr/Documents/Projects/ZonoOpt/src/Zono.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Zono() [1/2]

◆ Zono() [2/2]

◆ ~Zono()

Member Function Documentation

◆ clone()

◆ convert_form()

◆ do_bounding_box()

◆ do_is_empty()

◆ do_support()

◆ get_volume()

◆ print()

◆ reduce_order()

◆ set()