Rectangular set over an arbitrary number of dimensions. More...

#include <RectSet.h>

Inheritance diagram for lucid::RectSet:

Public Member Functions
	RectSet (Vector lb, Vector ub)
	Construct a rectangular set from lower and upper bounds.

	RectSet (std::initializer_list< Scalar > lb, std::initializer_list< Scalar > ub)
	Construct a rectangular set from lower and upper bounds.

	RectSet (const std::vector< std::pair< Scalar, Scalar > > &bounds)
	Construct a rectangular set from lower and upper bounds.

	RectSet (std::initializer_list< std::pair< Scalar, Scalar > > bounds)
	Construct a rectangular set from lower and upper bounds.

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

const Vector &	lower_bound () const
	Get read-only access to the lower bound of the rectangular set.

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

const Vector &	upper_bound () const
	Get read-only access to the upper bound of the rectangular set.

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

Vector	sizes () const
	Get read-only access to the size for each dimension of the rectangular set.

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	change_size (ConstVectorRef delta_size) override
	Change the size of the set.

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

RectSet	relative_to (const RectSet &set) const
	Compute the rectangular set relative to another rectangular set.

RectSet	relative_to (ConstVectorRef point) const
	Compute the rectangular set relative a new origin point.

RectSet	scale (ConstVectorRef scale) const
	Scale the rectangular set by the given factor(s).

RectSet	scale (double scale) const
	Scale the rectangular set by the given factor.

RectSet	scale (ConstVectorRef scale, const RectSet &bounds, bool relative_to_bounds=false) const
	Scale the rectangular set by the given factor(s) while keeping it inside the given bounds.

RectSet	scale (double scale, const RectSet &bounds, bool relative_to_bounds=false) const
	Scale the rectangular set by the given factor while keeping it inside the given bounds.

	operator Matrix () const
	Convert the rectangular set to a matrix representation.

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

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

void	change_size (double 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.

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.

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

virtual std::unique_ptr< Set >	to_anisotropic () const
	Create a new anisotropic 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 \( \texttip{x}{Element of the vector space} \).

Private Member Functions
std::unique_ptr< Set >	scale_wrapped_impl (ConstVectorRef scale, const RectSet &bounds, bool relative_to_bounds) const override
	Scale the rectangular set by the given factor while keeping it inside the given bounds.

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

Private Attributes
Vector	lb_
	Lower bound vector.

Vector	ub_
	Upper bound vector.

Detailed Description

Rectangular set over an arbitrary number of dimensions.

A vector \( \texttip{x}{Element of the vector space} \) is in the set if \( lb_i \le x_i \le ub_i \) for all components of the vector.

Constructor & Destructor Documentation

◆ RectSet() [1/4]

lucid::RectSet::RectSet	(	Vector	lb,
		Vector	ub )

Construct a rectangular set from lower and upper bounds.

Both bounds must belong to the same vector space.

Parameters

lb	lower bound vector
ub	upper bound vector

◆ RectSet() [2/4]

lucid::RectSet::RectSet	(	std::initializer_list< Scalar >	lb,
		std::initializer_list< Scalar >	ub )

Construct a rectangular set from lower and upper bounds.

Both bounds must belong to the same vector space.

Parameters

lb	lower bound vector
ub	upper bound vector

◆ RectSet() [3/4]

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

explicit

Construct a rectangular set from lower and upper bounds.

Both bounds must belong to the same vector space.

Parameters

bounds vector of pairs of lower and upper bounds

◆ RectSet() [4/4]

lucid::RectSet::RectSet ( std::initializer_list< std::pair< Scalar, Scalar > > bounds )

Construct a rectangular set from lower and upper bounds.

Both bounds must belong to the same vector space.

Parameters

bounds vector of pairs of lower and upper bounds

Member Function Documentation

◆ change_size() [1/2]

void lucid::RectSet::change_size ( ConstVectorRef delta_size )

overridevirtual

Change the size of the set.

The size change can be different for each dimension. For example, for a rectangular set, this would change the lower and upper bounds so that the original set sits in the center of the new set, which has its size changed by the specified amounts.

Precondition: The set must support size changes.; The size of delta_size must be equal to the dimension of the set.; The new size must be non-negative in all dimensions.

Parameters

delta_size vector of amounts to change the size of the set for each dimension

Reimplemented from lucid::Set.

◆ change_size() [2/2]

void lucid::Set::change_size ( double delta_size )

Change the size of the set.

The size change can be different for each dimension. For example, for a rectangular set, this would change the lower and upper bounds so that the original set sits in the center of the new set, which has its size changed by the specified amounts.

Precondition: The set must support size changes.; The new size must be non-negative in all dimensions.

Parameters

delta_size amount to change the size of the set

◆ clone()

std::unique_ptr< Set > lucid::RectSet::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.

◆ dimension()

Dimension lucid::RectSet::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.

◆ general_lower_bound()

Vector lucid::RectSet::general_lower_bound ( ) const

inlinenodiscardoverridevirtual

Get read-only access to the lower bound of the smallest rectangular set including the whole set.

Returns: lower bound of the smallest rectangular set including the whole set

Reimplemented from lucid::Set.

◆ general_upper_bound()

Vector lucid::RectSet::general_upper_bound ( ) const

inlinenodiscardoverridevirtual

Get read-only access to the upper bound of the smallest rectangular set including the whole set.

Returns: upper bound of the smallest rectangular set including the whole set

Reimplemented from lucid::Set.

◆ increase_size_impl()

void lucid::RectSet::increase_size_impl ( ConstVectorRef size_increase )

overrideprivatevirtual

Increase the size of the set.

The size increase can be different for each dimension. The increase is applied symmetrically around the center of the set such that the total size after the increase is equal to the original size plus size_increase.

Precondition: The set must support size changes.; The size of scale must be equal to the dimension of the set.; The new size must be non-negative in all dimensions.

Parameters

size_increase amount to increase the size of the set for each dimension

Reimplemented from lucid::Set.

◆ lattice() [1/2]

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

nodiscardoverridevirtual

Generate a lattice of points in the set.

In python, this would be implemented as:

import numpy as np
 
def build_lattice(points_per_dim, endpoint):
   # self.lb_ and self.ub_ are the lower and upper bounds of the rectangular set
   grids = [np.linspace(l, u, n, endpoint) for l, u, n in zip(self.lb_, self.ub_, points_per_dim)]
   mesh = np.meshgrid(*grids, indexing="xy")
   pts = np.vstack([m.ravel() for m in mesh]).T
   return pts

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

◆ lower_bound()

const Vector & lucid::RectSet::lower_bound ( ) const

inlinenodiscard

Get read-only access to the lower bound of the rectangular set.

Returns: lower bound of the rectangular set

◆ operator Matrix()

lucid::RectSet::operator Matrix ( ) const

Convert the rectangular set to a matrix representation.

Returns: matrix where the first row contains lower bounds and the second row contains upper bounds

◆ operator()()

bool lucid::RectSet::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.

◆ relative_to() [1/2]

RectSet lucid::RectSet::relative_to ( const RectSet & set ) const

nodiscard

Compute the rectangular set relative to another rectangular set.

Instead of absolute coordinates, the new rectangular set will be expressed in coordinates relative to the lower bound of the other rectangular set.

Precondition: The two rectangular sets must have the same dimension.

Parameters

set	other rectangular set

Returns: new rectangular set expressed in relative coordinates

◆ relative_to() [2/2]

RectSet lucid::RectSet::relative_to ( ConstVectorRef point ) const

nodiscard

Compute the rectangular set relative a new origin point.

Instead of absolute coordinates, the new rectangular set will be expressed in coordinates relative to the given point.

Precondition: The point must have the same dimension as the rectangular set.

Parameters

point point representing the new origin

Returns: new rectangular set expressed in relative coordinates

◆ sample()

Matrix lucid::RectSet::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() [1/4]

RectSet lucid::RectSet::scale ( ConstVectorRef scale ) const

nodiscard

Scale the rectangular set by the given factor(s).

The scaling is performed with respect to the center of the rectangular set.

Parameters

scale scaling factor(s) for each dimension

Returns: new scaled rectangular set

◆ scale() [2/4]

RectSet lucid::RectSet::scale	(	ConstVectorRef	scale,
		const RectSet &	bounds,
		bool	relative_to_bounds = false ) const

nodiscard

Scale the rectangular set by the given factor(s) while keeping it inside the given bounds.

The scaling is performed with respect to the center of the rectangular set. The scaling factor can be computed relative to either

the current size of the rectangular set;

the size of the bounding rectangular set.

Parameters

scale	scaling factor(s) for each dimension
bounds	bounding rectangular set
relative_to_bounds	if true, the scaling factor is computed relative to the size of the bounding rectangular set; if false, the scaling factor is computed relative to the current size of the rectangular

Returns: new scaled rectangular set

◆ scale() [3/4]

RectSet lucid::RectSet::scale ( double scale ) const

nodiscard

Scale the rectangular set by the given factor.

The scaling is performed with respect to the center of the rectangular set.

Parameters

scale scaling factor

Returns: new scaled rectangular set

◆ scale() [4/4]

RectSet lucid::RectSet::scale	(	double	scale,
		const RectSet &	bounds,
		bool	relative_to_bounds = false ) const

nodiscard

Scale the rectangular set by the given factor while keeping it inside the given bounds.

The scaling is performed with respect to the center of the rectangular set. The scaling factor can be computed relative to either

the current size of the rectangular set;

the size of the bounding rectangular set.

Parameters

scale	scaling factor
bounds	bounding rectangular set
relative_to_bounds	if true, the scaling factor is computed relative to the size of the bounding rectangular set; if false, the scaling factor is computed relative to the current size of the rectangular

Returns: new scaled rectangular set

◆ scale_wrapped_impl()

std::unique_ptr< Set > lucid::RectSet::scale_wrapped_impl	(	ConstVectorRef	scale,
		const RectSet &	bounds,
		bool	relative_to_bounds ) const

nodiscardoverrideprivatevirtual

Scale the rectangular set by the given factor while keeping it inside the given bounds.

If any dimension exceeds the bounds after scaling, it is wrapped around to the other side, as another rectangular set. The scaling is performed with respect to the center of the rectangular set. The scaling factor can be computed relative to either

the current size of the rectangular set;

the size of the bounding rectangular set.

Parameters

scale	scaling factor
bounds	bounding rectangular set
relative_to_bounds	if true, the scaling factor is computed relative to the size of the bounding rectangular set; if false, the scaling factor is computed relative to the current size of the rectangular

Returns: new scaled rectangular set

Reimplemented from lucid::Set.

◆ sizes()

Vector lucid::RectSet::sizes ( ) const

inlinenodiscard

Get read-only access to the size for each dimension of the rectangular set.

Returns: size for each dimension of the rectangular set

◆ to_rect_set()

std::unique_ptr< Set > lucid::RectSet::to_rect_set ( ) const

nodiscardoverridevirtual

Convert the set to a rectangular set.

Not all sets can be converted to rectangular sets. If the set cannot be converted, an exception is thrown.

Returns: unique pointer to the rectangular set

Reimplemented from lucid::Set.

◆ to_string()

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

nodiscardoverridevirtual

Obtain the string representation of this object.

Returns: string representation of this object

Reimplemented from lucid::Set.

◆ upper_bound()

const Vector & lucid::RectSet::upper_bound ( ) const

inlinenodiscard

Get read-only access to the upper bound of the rectangular set.

Returns: upper bound of the rectangular set

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

lucid/model/RectSet.h
lucid/model/RectSet.cpp

Public Member Functions

Private Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ RectSet() [1/4]

◆ RectSet() [2/4]

◆ RectSet() [3/4]

◆ RectSet() [4/4]

Member Function Documentation

◆ change_size() [1/2]

◆ change_size() [2/2]

◆ clone()

◆ dimension()

◆ general_lower_bound()

◆ general_upper_bound()

◆ increase_size_impl()

◆ lattice() [1/2]

◆ lattice() [2/2]

◆ lower_bound()

◆ operator Matrix()

◆ operator()()

◆ relative_to() [1/2]

◆ relative_to() [2/2]

◆ sample()

◆ scale() [1/4]

◆ scale() [2/4]

◆ scale() [3/4]

◆ scale() [4/4]

◆ scale_wrapped_impl()

◆ sizes()

◆ to_rect_set()

◆ to_string()

◆ upper_bound()