lucid::ValleePoussinKernel Class Reference

Vallée-Poussin kernel. More...

#include <ValleePoussinKernel.h>

Inheritance diagram for lucid::ValleePoussinKernel:

Public Member Functions
	ValleePoussinKernel (double a=1.0, double b=1.0)
	Construct a new ValleePoussinKernel object with the given parameters.
bool	is_stationary () const override
	Check whether the kernel is is stationary.
double	a () const
	Get read-only access to the a parameter of the kernel.
double	b () const
	Get read-only access to the b parameter of the kernel.
double	get_d (Parameter parameter) const override
	Get the value of the specified parameter.
void	set (Parameter parameter, double value) override
	Set the parameter to the indicated value.
std::unique_ptr< Kernel >	clone () const override
	Clone the kernel.
std::string	to_string () const override
	Get string representation of the kernel.
Public Member Functions inherited from lucid::Kernel
template<class DerivedX, class DerivedY>
Matrix	operator() (const MatrixBase< DerivedX > &x1, const MatrixBase< DerivedY > &x2) const
	Compute the kernel function on \( x_1 \) and \( x_2 \), both being matrices of row vectors in \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.
template<class Derived>
Matrix	operator() (const MatrixBase< Derived > &x) const
	Compute the kernel function on \( \texttip{x}{Element of the vector space} \), which is a matrix of row vectors in \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.
template<class Derived>
Matrix	operator() (const MatrixBase< Derived > &x, std::vector< Matrix > &gradient) const
	Compute the kernel function on \( \texttip{x}{Element of the vector space} \), which is a matrix of row vectors in \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.
Public Member Functions inherited from lucid::Parametrizable
template<IsAnyOf< int, double, const Vector & > T>
T	get (Parameter parameter) const
	Get the value of the specified parameter.
template<Parameter P>
internal::ParameterType< P >::ref_type	get () const
	Get the value of the specified parameter.
std::variant< int, double, Vector >	get (Parameter parameter) const
	Get the value of the specified parameter.
void	set (Parameter parameter, const std::variant< int, double, Vector > &value)
	Set the parameter to the indicated value.
template<Parameter P>
void	set (const std::variant< int, double, Vector > &value)
	Set the parameter to the indicated value.
void	set (Parameter parameter, std::size_t idx, const std::variant< std::vector< int >, std::vector< double >, std::vector< Vector > > &values)
	Set the parameter to the index-th value among the indicated values.
template<Parameter P>
void	set (std::size_t idx, const std::variant< std::vector< int >, std::vector< double >, std::vector< Vector > > &values)
	Set the parameter to the index-th value among the indicated values.
virtual void	set (Parameter parameter, int value)
	Set the parameter to the indicated value.
virtual void	set (Parameter parameter, const Vector &value)
	Set the parameter to the indicated value.
template<Parameter P>
void	set (typename internal::ParameterType< P >::ref_type value)
	Set the parameter to the indicated value.
bool	has (const Parameter parameter) const
	Check whether the parameter is present in this object.
Parameters	parameters () const
	Get read-only access to the parameters of the parametrizable object.
std::vector< Parameter >	parameters_list () const
	Get read-only access to the list of parameters of the parametrizable object.
Parametrizable &	load (const Parametrizable &o)
	Load parameters from another Parametrizable object.

Private Member Functions
Matrix	apply_impl (ConstMatrixRef x1, ConstMatrixRef x2, std::vector< Matrix > *gradient) const override
	Concrete implementation of operator()().

Private Attributes
double	a_
	'a' parameter
double	b_
	'b' parameter

Additional Inherited Members
Protected Member Functions inherited from lucid::Kernel
Matrix	operator() (ConstMatrixRef x1, ConstMatrixRef x2, std::vector< Matrix > *gradient) const
	Compute the kernel function on \( x_1 \) and \( x_2 \), both being matrices of row vectors in \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.
Protected Member Functions inherited from lucid::Parametrizable
virtual int	get_i (Parameter parameter) const
	Get the value of the specified parameter.
virtual const Vector &	get_v (Parameter parameter) const
	Get the value of the specified parameter.
Protected Attributes inherited from lucid::Parametrizable
Parameters	parameters_
	Parameters supported by this object.

Detailed Description

Vallée-Poussin kernel.

Given a vector space \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^n \) and a vector \( x \in \mathcal{X} \), the Vallee-Poussin kernel \( k_{a,b}^n : \mathcal{X} \to \mathbb{R} \) with parameters \( a, b \in \mathbb{R} \) is defined as

\[k_{a,b}^n(x) = \frac{1}{(b - a)^n} \prod_{i=1}^{n} \frac{ \sin\left( \frac{b + a}{2} x_i \right) \sin\left( \frac{b - a}{2} x_i \right) }{ \sin^2{\left( \frac{x_i}{2} \right)} } \]

Constructor & Destructor Documentation

ValleePoussinKernel()

lucid::ValleePoussinKernel::ValleePoussinKernel ( double a = 1.0, double b = 1.0 )

explicit

Construct a new ValleePoussinKernel object with the given parameters.

Parameters

a	parameter
b	parameter

Member Function Documentation

a()

double lucid::ValleePoussinKernel::a ( ) const

inlinenodiscard

Get read-only access to the a parameter of the kernel.

Returns

a parameter of the kernel

apply_impl()

Matrix lucid::ValleePoussinKernel::apply_impl ( ConstMatrixRef x1, ConstMatrixRef x2, std::vector< Matrix > * gradient ) const

overrideprivatevirtual

Concrete implementation of operator()().

Parameters

	x1	\( \texttip{n_1}{Number of samples in the first matrix} \times \texttip{d}{Dimension of the vector space} \) first input matrix
	x2	\( \texttip{n_2}{Number of samples in the second matrix} \times \texttip{d}{Dimension of the vector space} \) second input matrix
[out]	gradient	pointer to store the gradient of the kernel function with respect to the kernel parameters

Returns

kernel value

Implements lucid::Kernel.

b()

double lucid::ValleePoussinKernel::b ( ) const

inlinenodiscard

Get read-only access to the b parameter of the kernel.

Returns

b parameter of the kernel

clone()

std::unique_ptr< Kernel > lucid::ValleePoussinKernel::clone ( ) const

nodiscardoverridevirtual

Clone the kernel.

Create a new instance of the kernel with the same parameters.

Returns

new instance of the kernel

Implements lucid::Kernel.

get_d()

double lucid::ValleePoussinKernel::get_d ( Parameter parameter ) const

nodiscardoverridevirtual

Get the value of the specified parameter.

Parameters

parameter

parameter to retrieve

Returns

value of the parameter

Precondition

The parameter must be present and be associated with a value of type double.

Reimplemented from lucid::Parametrizable.

is_stationary()

bool lucid::ValleePoussinKernel::is_stationary ( ) const

inlinenodiscardoverridevirtual

Check whether the kernel is is stationary.

Returns

true if the kernel is is stationary

false if the kernel is not is stationary

Implements lucid::Kernel.

set()

void lucid::ValleePoussinKernel::set ( Parameter parameter, double value )

overridevirtual

Set the parameter to the indicated value.

Parameters

parameter	parameter to set
value	value to assign to the specified parameter

Precondition

The parameter must be present and be associated with a value of type double.

Reimplemented from lucid::Parametrizable.

to_string()

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

nodiscardoverridevirtual

Get string representation of the kernel.

Returns

string representation Obtain the string representation of this object.

string representation of this object

Reimplemented from lucid::Kernel.

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

• lucid/model/ValleePoussinKernel.h
• lucid/model/ValleePoussinKernel.cpp