A convex polytope set in half-space representation. More...

#include <PolytopeSet.h>

Inheritance diagram for lucid::PolytopeSet:

Public Member Functions
	PolytopeSet (Matrix A, Vector b)
	Construct a polytope from hyperplane normals and offsets.

	PolytopeSet (std::initializer_list< std::initializer_list< Scalar > > A, std::initializer_list< Scalar > b)
	Construct a polytope from hyperplane normals and offsets.

Dimension	dimension () const override
	Get read-only access to the dimension of the set \( \texttip{\mathcal{X}}{Polish sample vector space} \).

Matrix	sample (Index num_samples) const override
	Extract \( N \) elements from \( \texttip{\mathcal{X}}{Polish sample vector space} \) using some kind of random distribution.

bool	operator() (ConstVectorRef x) const override
	Check if a vector is in \( \texttip{\mathcal{X}}{Polish sample vector space} \).

Matrix	lattice (const VectorI &points_per_dim, bool endpoint) const override
	Generate a lattice of points in the set.

void	scale (Scalar factor)
	Scale the polytope by a factor.

const Matrix &	A () const
	Get read-only access to the hyperplane normals matrix of the polytope.

const Vector &	b () const
	Get read-only access to the hyperplane offsets vector of the polytope.

std::string	to_string () const override
	Obtain the string representation of this object.

std::unique_ptr< Set >	clone () const override
	Clone the set.

Matrix	lattice (Index points_per_dim, bool endpoint=false) const
	Generate a lattice of points in the set.

Public Member Functions inherited from lucid::Set
Vector	sample () const
	Extract an element from \( \texttip{\mathcal{X}}{Polish sample vector space} \) using some kind of random distribution.

bool	contains (ConstVectorRef x) const
	Check if a vector is in \( \texttip{\mathcal{X}}{Polish sample vector space} \).

bool	contains_wrapped (ConstVectorRef x, ConstVectorRef period, Dimension num_periods) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

bool	contains_wrapped (ConstVectorRef x, ConstVectorRef period, const std::vector< Dimension > &num_periods) const
	Check if a vector is in \( \texttip{\mathcal{X}}{Polish sample vector space} \), having the vector wrapped around a given period.

bool	contains_wrapped (ConstVectorRef x, ConstVectorRef period, Dimension num_periods_below, Dimension num_periods_above) const
	This is an overloaded member function, provided for convenience. It differs from the above function only in what argument(s) it accepts.

bool	contains_wrapped (ConstVectorRef x, ConstVectorRef period, const std::vector< Dimension > &num_periods_below, const std::vector< Dimension > &num_periods_above) const
	Check if a vector is in \( \texttip{\mathcal{X}}{Polish sample vector space} \), having the vector wrapped around a given period.

bool	contains_wrapped (ConstVectorRef x, ConstVectorRef period) const
	Check if a vector is in \( \texttip{\mathcal{X}}{Polish sample vector space} \), having the vector wrapped around a given period.

Matrix	include (ConstMatrixRef xs) const
	Filter a set `xs`, returning only the row vectors that are in \( \texttip{\mathcal{X}}{Polish sample vector space} \).

std::vector< Index >	include_mask (ConstMatrixRef xs) const
	Filter a set `xs`, returning a mask containing the indices corresponding to the row vectors that are in \( \texttip{\mathcal{X}}{Polish sample vector space} \).

std::vector< Index >	include_mask_wrapped (ConstMatrixRef xs, ConstVectorRef period) const
	Filter a set `xs`, returning a mask containing the indices corresponding to the row vectors that are in \( \texttip{\mathcal{X}}{Polish sample vector space} \), accounting for wrapping around a given period.

Matrix	exclude (ConstMatrixRef xs) const
	Filter `xs`, return only the row vectors that are NOT in \( \texttip{\mathcal{X}}{Polish sample vector space} \).

std::vector< Index >	exclude_mask (ConstMatrixRef xs) const
	Filter a set `xs`, returning a mask containing the indices corresponding to the row vectors that are NOT in \( \texttip{\mathcal{X}}{Polish sample vector space} \).

std::vector< Index >	exclude_mask_wrapped (ConstMatrixRef xs, ConstVectorRef period) const
	Filter a set `xs`, returning a mask containing the indices corresponding to the row vectors that are NOT in \( \texttip{\mathcal{X}}{Polish sample vector space} \), accounting for wrapping around a given period.

std::pair< std::vector< Index >, std::vector< Index > >	include_exclude_masks (ConstMatrixRef xs) const
	Filter a set `xs`, returning masks containing the indices corresponding to the row vectors that are in \( \texttip{\mathcal{X}}{Polish sample vector space} \) and NOT in \( \texttip{\mathcal{X}}{Polish sample vector space} \).

std::pair< std::vector< Index >, std::vector< Index > >	include_exclude_masks_wrapped (ConstMatrixRef xs, ConstVectorRef period) const
	Filter a set `xs`, returning masks containing the indices corresponding to the row vectors that are in \( \texttip{\mathcal{X}}{Polish sample vector space} \) and NOT in \( \texttip{\mathcal{X}}{Polish sample vector space} \), accounting for wrapping around a given period.

std::pair< std::vector< Index >, std::vector< Index > >	include_exclude_masks_wrapped (ConstMatrixRef xs, const RectSet &period) const
	Filter a set `xs`, returning masks containing the indices corresponding to the row vectors that are in \( \texttip{\mathcal{X}}{Polish sample vector space} \) and NOT in \( \texttip{\mathcal{X}}{Polish sample vector space} \), accounting for wrapping around a given period.

std::unique_ptr< Set >	scale_wrapped (double scale, const RectSet &bounds, bool relative_to_bounds=false) const
	Scale the set by the given factor while keeping it inside the given bounds.

std::unique_ptr< Set >	scale_wrapped (ConstVectorRef scale, const RectSet &bounds, bool relative_to_bounds=false) const
	Scale the set by the given factor while keeping it inside the given bounds.

template<bool Inplace = false> requires (!Inplace)
std::unique_ptr< Set >	increase_size (ConstVectorRef size_increase) const
	Increase the size of the set.

template<bool Inplace = false> requires (Inplace)
void	increase_size (ConstVectorRef size_increase)
	Increase the size of the set.

void	change_size (double delta_size)
	Change the size of the set.

virtual void	change_size (ConstVectorRef delta_size)
	Change the size of the set.

Matrix	lattice (Index points_per_dim, bool endpoint=false) const
	Generate a lattice of points in the set.

virtual std::unique_ptr< Set >	to_rect_set () const
	Convert the set to a rectangular set.

virtual std::unique_ptr< Set >	to_anisotropic () const
	Create a new anisotropic set.

virtual Vector	general_lower_bound () const
	Get read-only access to the lower bound of the smallest rectangular set including the whole set.

virtual Vector	general_upper_bound () const
	Get read-only access to the upper bound of the smallest rectangular set including the whole set.

template<class Derived>
Eigen::MatrixBase< Derived > &	operator>> (Eigen::MatrixBase< Derived > &x) const
	Extract \( N \) elements element from \( \texttip{\mathcal{X}}{Polish sample vector space} \) using some kind of random distribution, where \( N \) is the number of rows in \( \texttip{x}{Element of the vector space} \).

Static Public Member Functions
static PolytopeSet	from_box (const std::vector< std::pair< Scalar, Scalar > > &bounds)
	Create a polytope from a bounding box (hyperrectangle).

Private Member Functions
std::pair< Vector, Vector >	compute_bounding_box () const
	Compute bounding box of the polytope using linear programming.

Private Attributes
Matrix	A_
	Hyperplane normals matrix (m x n)

Vector	b_
	Hyperplane offsets vector (m)

std::optional< std::pair< Vector, Vector > >	bbox_
	Cached bounding box.

Additional Inherited Members
Protected Member Functions inherited from lucid::Set
virtual std::unique_ptr< Set >	scale_wrapped_impl (ConstVectorRef scale, const RectSet &bounds, bool relative_to_bounds) const
	Scale the rectangular set by the given factor while keeping it inside the given bounds.

virtual void	increase_size_impl (ConstVectorRef size_increase)
	Increase the size of the set.

Detailed Description

A convex polytope set in half-space representation.

A vector \( \texttip{x}{Element of the vector space} \) is in the set if \( A x \le b \), where \( A \) is a matrix of hyperplane normals and \( b \) is a vector of hyperplane offsets.

Constructor & Destructor Documentation

◆ PolytopeSet() [1/2]

lucid::PolytopeSet::PolytopeSet	(	Matrix	A,
		Vector	b )

Construct a polytope from hyperplane normals and offsets.

Parameters

A	matrix of hyperplane normals (each row is a normal vector)
b	vector of hyperplane offsets

◆ PolytopeSet() [2/2]

lucid::PolytopeSet::PolytopeSet	(	std::initializer_list< std::initializer_list< Scalar > >	A,
		std::initializer_list< Scalar >	b )

Construct a polytope from hyperplane normals and offsets.

Parameters

A	matrix of hyperplane normals (each row is a normal vector)
b	vector of hyperplane offsets

Member Function Documentation

◆ A()

const Matrix & lucid::PolytopeSet::A ( ) const

inlinenodiscard

Get read-only access to the hyperplane normals matrix of the polytope.

Returns: hyperplane normals matrix of the polytope

◆ b()

const Vector & lucid::PolytopeSet::b ( ) const

inlinenodiscard

Get read-only access to the hyperplane offsets vector of the polytope.

Returns: hyperplane offsets vector of the polytope

◆ clone()

std::unique_ptr< Set > lucid::PolytopeSet::clone ( ) const

nodiscardoverridevirtual

Clone the set.

Create a new instance of the set with the same properties as the current one.

Returns: new instance of the set

Implements lucid::Set.

◆ compute_bounding_box()

std::pair< Vector, Vector > lucid::PolytopeSet::compute_bounding_box ( ) const

private

Compute bounding box of the polytope using linear programming.

Returns: pair of lower and upper bounds

◆ dimension()

Dimension lucid::PolytopeSet::dimension ( ) const

inlinenodiscardoverridevirtual

Get read-only access to the dimension of the set \( \texttip{\mathcal{X}}{Polish sample vector space} \).

Returns: dimension of the set \( \texttip{\mathcal{X}}{Polish sample vector space} \)

Implements lucid::Set.

◆ from_box()

PolytopeSet lucid::PolytopeSet::from_box ( const std::vector< std::pair< Scalar, Scalar > > & bounds )

static

Create a polytope from a bounding box (hyperrectangle).

Parameters

bounds vector of pairs of lower and upper bounds

Returns: polytope representing the hyperrectangle

◆ lattice() [1/2]

Matrix lucid::PolytopeSet::lattice	(	const VectorI &	points_per_dim,
		bool	endpoint ) const

nodiscardoverridevirtual

Generate a lattice of points in the set.

Parameters

points_per_dim	number of points per each dimension
endpoint	whether to include the endpoints of the lattice

Returns: lattice of points in the set

Implements lucid::Set.

◆ lattice() [2/2]

Matrix lucid::Set::lattice	(	Index	points_per_dim,
		bool	endpoint = false ) const

nodiscard

Generate a lattice of points in the set.

Parameters

points_per_dim	number of points per each dimension
endpoint	whether to include the endpoints of the lattice

Returns: lattice of points in the set

◆ operator()()

bool lucid::PolytopeSet::operator() ( ConstVectorRef x ) const

nodiscardoverridevirtual

Check if a vector is in \( \texttip{\mathcal{X}}{Polish sample vector space} \).

Precondition: \( \texttip{x}{Element of the vector space} \) must have the same dimension as the set

Parameters

x	vector to test

Returns: true if \( \texttip{x}{Element of the vector space} \) is in the set; false if \( \texttip{x}{Element of the vector space} \) is not in the set

Implements lucid::Set.

◆ sample()

Matrix lucid::PolytopeSet::sample ( Index num_samples ) const

nodiscardoverridevirtual

Extract \( N \) elements from \( \texttip{\mathcal{X}}{Polish sample vector space} \) using some kind of random distribution.

Note: The seed for the random number generator can be set using random::seed.

Precondition: num_samples must be greater than 0

Parameters

num_samples number of samples to generate \( N \)

Returns: \( \texttip{n}{Number of samples} \times \texttip{d}{Dimension of the vector space} \) matrix of samples, where \( \texttip{d}{Dimension of the vector space} \) is the dimension of \( \texttip{\mathcal{X}}{Polish sample vector space} \). In other words, the samples are stored as rows vectors in the matrix

Implements lucid::Set.

◆ scale()

void lucid::PolytopeSet::scale ( Scalar factor )

Scale the polytope by a factor.

The constraints \( A x \le b \) are scaled to \( A x \le s b \).

Parameters

factor scaling factor \( s \)

◆ to_string()

std::string lucid::PolytopeSet::to_string ( ) const

nodiscardoverridevirtual

Obtain the string representation of this object.

Returns: string representation of this object

Reimplemented from lucid::Set.

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

lucid/model/PolytopeSet.h
lucid/model/PolytopeSet.cpp

Public Member Functions

Static Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ PolytopeSet() [1/2]

◆ PolytopeSet() [2/2]

Member Function Documentation

◆ A()

◆ b()

◆ clone()

◆ compute_bounding_box()

◆ dimension()

◆ from_box()

◆ lattice() [1/2]

◆ lattice() [2/2]

◆ operator()()

◆ sample()

◆ scale()

◆ to_string()