Multidimensional ellipsoid set. More...

#include <EllipseSet.h>

Inheritance diagram for lucid::EllipseSet:

Public Member Functions
	EllipseSet (ConstVectorRef center, ConstVectorRef radii)
	Construct an ellipsoid set from a `center` and a vector of `radii`.

	EllipseSet (ConstVectorRef center, Scalar radius)
	Construct an ellipsoid set from a `center` and a uniform `radius`.

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

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

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 \( \texttip{\mathcal{X}}{Polish sample vector space} \).

const Vector &	center () const
	Get read-only access to the center of the ellipsoid set.

const Vector &	radii () const
	Get read-only access to the radii of the ellipsoid set.

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

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

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

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

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

void	change_size (double delta_size)
	Change the size of 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 \( \texttip{x}{Element of the vector space} \).

Public Attributes
Vector	center_
	Center of the ellipsoid. Determines the dimension of the ellipsoid set.

Vector	radii_
	Radii for each dimension.

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.

Detailed Description

Multidimensional ellipsoid set.

A vector \( \texttip{x}{Element of the vector space} \) is in the set if \( \sum_{i=1}^{d} \left(\frac{x_i - c_i}{r_i}\right)^2 \le 1 \), where \( c \) is the center and \( r \) is the vector of radii. The sampling is uniform over the volume of the ellipse. The samples are generated using an adapted version of the Muller method.

Constructor & Destructor Documentation

◆ EllipseSet() [1/2]

lucid::EllipseSet::EllipseSet	(	ConstVectorRef	center,
		ConstVectorRef	radii )

Construct an ellipsoid set from a center and a vector of radii.

The dimension of the space the ellipsoid set lives in is determined by the size of the center vector.

Parameters

center	vector representing the center of the ellipsoid
radii	vector of radii for each dimension

◆ EllipseSet() [2/2]

lucid::EllipseSet::EllipseSet	(	ConstVectorRef	center,
		Scalar	radius )

Construct an ellipsoid set from a center and a uniform radius.

This creates a sphere (all radii are equal). The dimension of the space the ellipsoid set lives in is determined by the size of the center vector.

Parameters

center	vector representing the center of the ellipsoid
radius	uniform radius for all dimensions

Member Function Documentation

◆ center()

const Vector & lucid::EllipseSet::center ( ) const

inlinenodiscard

Get read-only access to the center of the ellipsoid set.

Returns: center of the ellipsoid set

◆ change_size() [1/2]

void lucid::EllipseSet::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::EllipseSet::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::EllipseSet::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::EllipseSet::general_lower_bound ( ) const

nodiscardoverridevirtual

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::EllipseSet::general_upper_bound ( ) const

nodiscardoverridevirtual

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::EllipseSet::increase_size_impl ( ConstVectorRef size_increase )

overridevirtual

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()

Matrix lucid::EllipseSet::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.

◆ operator()()

bool lucid::EllipseSet::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.

◆ radii()

const Vector & lucid::EllipseSet::radii ( ) const

inlinenodiscard

Get read-only access to the radii of the ellipsoid set.

Returns: radii of the ellipsoid set

◆ sample()

Matrix lucid::EllipseSet::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.

◆ to_rect_set()

std::unique_ptr< Set > lucid::EllipseSet::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::EllipseSet::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/EllipseSet.h
lucid/model/EllipseSet.cpp

Public Member Functions

Public Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ EllipseSet() [1/2]

◆ EllipseSet() [2/2]

Member Function Documentation

◆ center()

◆ change_size() [1/2]

◆ change_size() [2/2]

◆ clone()

◆ dimension()

◆ general_lower_bound()

◆ general_upper_bound()

◆ increase_size_impl()

◆ lattice()

◆ operator()()

◆ radii()

◆ sample()

◆ to_rect_set()

◆ to_string()