cmp::covariance::SquaredExponential Class Reference

Squared Exponential (RBF / Gaussian) covariance function. More...

#include <covariance.h>

Inheritance diagram for cmp::covariance::SquaredExponential:

Collaboration diagram for cmp::covariance::SquaredExponential:

Public Member Functions
	SquaredExponential (const SquaredExponential &)=default
	SquaredExponential (SquaredExponential &&)=default
SquaredExponential &	operator= (const SquaredExponential &)=default
SquaredExponential &	operator= (SquaredExponential &&)=default
	SquaredExponential (const size_t &index, const int &indexX=-1)
double	eval (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2, const Eigen::VectorXd &par) const
double	evalGradient (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2, const Eigen::VectorXd &par, const size_t &i) const
double	evalHessian (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2, const Eigen::VectorXd &par, const size_t &i, const size_t &j) const
Public Member Functions inherited from cmp::covariance::Covariance
virtual	~Covariance ()=default

Static Public Member Functions
static std::shared_ptr< Covariance >	make (const size_t &l, const int &i)

Private Attributes
size_t	index_
	Hyperparameter index for the lengthscale parameter.
int	indexX_
	Dimension index to evaluate, or -1 for the full isotropic kernel.

Detailed Description

Squared Exponential (RBF / Gaussian) covariance function.

Mathematical Formulation Evaluates the squared exponential kernel between two inputs \(\mathbf{x}_1, \mathbf{x}_2\):

\[ k(\mathbf{x}_1, \mathbf{x}_2) = \exp\left( -\frac{1}{2} \left(\frac{d}{\ell}\right)^2 \right) \]

where \(d\) is the distance (Euclidean norm \(\|\mathbf{x}_1 - \mathbf{x}_2\|_2\) if isotropic, or absolute coordinate distance \(|x_{1,i} - x_{2,i}|\) if restricted to dimension \(i\)), and \(\ell = \theta_{\text{index}}\) is the lengthscale hyperparameter.

Implementation Algorithm

1. Computes the distance \(d\) based on the component index configuration.
2. Computes the exponential kernel value.
3. Evaluates analytical first-order and second-order derivatives with respect to the lengthscale \(\ell\).

Constructor & Destructor Documentation

SquaredExponential() [1/3]

cmp::covariance::SquaredExponential::SquaredExponential ( const SquaredExponential &  )

default

SquaredExponential() [2/3]

cmp::covariance::SquaredExponential::SquaredExponential ( SquaredExponential &&  )

default

SquaredExponential() [3/3]

cmp::covariance::SquaredExponential::SquaredExponential ( const size_t &  index, const int &  indexX = -1  )

inline

Member Function Documentation

eval()

double cmp::covariance::SquaredExponential::eval ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2, const Eigen::VectorXd &  par  ) const

inlinevirtual

Implements cmp::covariance::Covariance.

evalGradient()

double cmp::covariance::SquaredExponential::evalGradient ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2, const Eigen::VectorXd &  par, const size_t &  i  ) const

inlinevirtual

Implements cmp::covariance::Covariance.

evalHessian()

double cmp::covariance::SquaredExponential::evalHessian ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2, const Eigen::VectorXd &  par, const size_t &  i, const size_t &  j  ) const

inlinevirtual

Implements cmp::covariance::Covariance.

make()

static std::shared_ptr< Covariance > cmp::covariance::SquaredExponential::make ( const size_t &  l, const int &  i  )

inlinestatic

operator=() [1/2]

SquaredExponential & cmp::covariance::SquaredExponential::operator= ( const SquaredExponential &  )

default

operator=() [2/2]

SquaredExponential & cmp::covariance::SquaredExponential::operator= ( SquaredExponential &&  )

default

Member Data Documentation

index_

size_t cmp::covariance::SquaredExponential::index_

private

Hyperparameter index for the lengthscale parameter.

indexX_

int cmp::covariance::SquaredExponential::indexX_

private

Dimension index to evaluate, or -1 for the full isotropic kernel.

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

• include/covariance.h