cmp::covariance::Matern52 Class Reference

Matérn covariance function with parameter nu = 5/2. More...

#include <covariance.h>

Inheritance diagram for cmp::covariance::Matern52:

Collaboration diagram for cmp::covariance::Matern52:

Public Member Functions
	Matern52 (const Matern52 &)=default
	Matern52 (Matern52 &&)=default
Matern52 &	operator= (const Matern52 &)=default
Matern52 &	operator= (Matern52 &&)=default
	Matern52 (const size_t &l, const int &i=-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

Matérn covariance function with parameter nu = 5/2.

Mathematical Formulation Evaluates the Matérn 5/2 kernel between two inputs \(\mathbf{x}_1, \mathbf{x}_2\):

\[ k(\mathbf{x}_1, \mathbf{x}_2) = \left( 1 + \frac{\sqrt{5}d}{\ell} + \frac{5d^2}{3\ell^2} \right) \exp\left( -\frac{\sqrt{5}d}{\ell} \right) \]

where \(d\) is the distance (isotropic or coordinate-based) and \(\ell = \theta_{\text{index}}\) is the lengthscale hyperparameter. This kernel yields processes that are twice differentiable.

Implementation Algorithm

1. Computes the distance \(d\).
2. Computes the polynomial coefficients and exponential scaling terms.
3. Evaluates analytical first-order and second-order derivatives with respect to \(\ell\).

Constructor & Destructor Documentation

Matern52() [1/3]

cmp::covariance::Matern52::Matern52 ( const Matern52 &  )

default

Matern52() [2/3]

cmp::covariance::Matern52::Matern52 ( Matern52 &&  )

default

Matern52() [3/3]

cmp::covariance::Matern52::Matern52 ( const size_t &  l, const int &  i = -1  )

inline

Member Function Documentation

eval()

double cmp::covariance::Matern52::eval ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2, const Eigen::VectorXd &  par  ) const

inlinevirtual

Implements cmp::covariance::Covariance.

evalGradient()

double cmp::covariance::Matern52::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::Matern52::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::Matern52::make ( const size_t &  l, const int &  i  )

inlinestatic

operator=() [1/2]

Matern52 & cmp::covariance::Matern52::operator= ( const Matern52 &  )

default

operator=() [2/2]

Matern52 & cmp::covariance::Matern52::operator= ( Matern52 &&  )

default

Member Data Documentation

index_

size_t cmp::covariance::Matern52::index_

private

Hyperparameter index for the lengthscale parameter.

indexX_

int cmp::covariance::Matern52::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