Represents a kernel function. More...

#include <Kernel.h>

Inheritance diagram for lucid::Kernel:

Public Member Functions
virtual bool	is_stationary () const =0
	Check whether the kernel is is stationary.

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 \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.

virtual std::unique_ptr< Kernel >	clone () const =0
	Clone the kernel.

virtual std::string	to_string () const
	Get string representation of the kernel.

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, double 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.

Protected Member Functions
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 \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.

virtual Matrix	apply_impl (ConstMatrixRef x1, ConstMatrixRef x2, std::vector< Matrix > *gradient) const =0
	Concrete implementation of operator()().

Protected Member Functions inherited from lucid::Parametrizable
virtual int	get_i (Parameter parameter) const
	Get the value of the specified `parameter`.

virtual double	get_d (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`.

Additional Inherited Members
Protected Attributes inherited from lucid::Parametrizable
Parameters	parameters_
	Parameters supported by this object.

Detailed Description

Represents a kernel function.

Given a vector space \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \), a kernel \( k : \mathcal{X} \times \mathcal{X} \to \mathbb{R} \) is a positive definite function that uniquely identifies a reproducing kernel Hilbert space (RKHS) \( \mathcal{H} \) that contains functions \( f : \mathcal{X} \to \mathbb{R} \). Moreover, we are guaranteed the property

\[f(x) = \langle f, k(x, \cdot) \rangle_\mathcal{H} \]

for all \( x \in \mathcal{X} \) and \( f \in \mathcal{H} \),

Member Function Documentation

◆ apply_impl()

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

protectedpure virtual

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

Implemented in lucid::GaussianKernel, and lucid::ValleePoussinKernel.

◆ clone()

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

nodiscardpure virtual

Clone the kernel.

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

Returns: new instance of the kernel

Implemented in lucid::GaussianKernel, and lucid::ValleePoussinKernel.

◆ is_stationary()

virtual bool lucid::Kernel::is_stationary ( ) const

nodiscardpure virtual

Check whether the kernel is is stationary.

Returns: true if the kernel is is stationary; false if the kernel is not is stationary

Implemented in lucid::GaussianKernel, and lucid::ValleePoussinKernel.

◆ operator()() [1/4]

template<class Derived>

Matrix lucid::Kernel::operator() ( const MatrixBase< Derived > & x ) const

inline

Compute the kernel function on \( \texttip{x}{Element of the vector space} \), which is a matrix of row vectors in \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.

\[k(x, x) . \]

Template Parameters

Derived type of the input matrix

Parameters

x	\( \texttip{n}{Number of samples} \times \texttip{d}{Dimension of the vector space} \) input matrix

Returns: kernel value

◆ operator()() [2/4]

template<class Derived>

Matrix lucid::Kernel::operator()	(	const MatrixBase< Derived > &	x,
		std::vector< Matrix > &	gradient ) const

inline

Compute the kernel function on \( \texttip{x}{Element of the vector space} \), which is a matrix of row vectors in \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.

\[k(x, x) . \]

Moreover, compute the gradient of the kernel function and store it in gradient.

Template Parameters

Derived type of the input matrix

Parameters

	x	\( \texttip{n}{Number of samples} \times \texttip{d}{Dimension of the vector space} \) input matrix
[out]	gradient	gradient of the kernel function with respect to the parameters dimensions

Returns: kernel value

◆ operator()() [3/4]

template<class DerivedX, class DerivedY>

Matrix lucid::Kernel::operator()	(	const MatrixBase< DerivedX > &	x1,
		const MatrixBase< DerivedY > &	x2 ) const

inline

Compute the kernel function on \( x_1 \) and \( x_2 \), both being matrices of row vectors in \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.

\[k(x_1, x_2) . \]

Precondition: x1 and x2 must have the same number of columns.

Template Parameters

DerivedX	type of the first input matrix
DerivedY	type of the second input matrix

Parameters

x1	\( \texttip{n_1}{Number of samples in the first matrix} \times \texttip{d}{Dimension of the vector space} \) first input row matrix
x2	\( \texttip{n_2}{Number of samples in the second matrix} \times \texttip{d}{Dimension of the vector space} \) second input row matrix

Returns: kernel value

◆ operator()() [4/4]

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

protected

Compute the kernel function on \( x_1 \) and \( x_2 \), both being matrices of row vectors in \( \texttip{\mathcal{X}}{Polish sample vector space} \subseteq \mathbb{R}^d \),.

\[k(x_1, x_2) . \]

If gradient is not nullptr, the gradient of the kernel function with respect to the parameters is computed and stored in *gradient.

Precondition: x1 and x2 must have the same number of columns.

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

◆ to_string()

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

nodiscardvirtual

Get string representation of the kernel.

Returns: string representation Obtain the string representation of this object.; string representation of this object

Reimplemented in lucid::GaussianKernel, and lucid::ValleePoussinKernel.

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

lucid/model/Kernel.h
lucid/model/Kernel.cpp

Public Member Functions

Protected Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation

◆ apply_impl()

◆ clone()

◆ is_stationary()

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

◆ to_string()