cmp::covariance::Matern Class Reference

General Matérn covariance function. More...

#include <covariance.h>

Inheritance diagram for cmp::covariance::Matern:

Collaboration diagram for cmp::covariance::Matern:

Public Member Functions
	Matern (const Matern &)=default
	Matern (Matern &&)=default
Matern &	operator= (const Matern &)=default
Matern &	operator= (Matern &&)=default
	Matern (const size_t &index, const double &nu, 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 double &nu, 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.
double	nu_
	Smoothness parameter nu.

Detailed Description

General Matérn covariance function.

Mathematical Formulation Evaluates the Matérn covariance function between two inputs \(\mathbf{x}_1, \mathbf{x}_2\):

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

where \(d\) is the distance, \(\ell = \theta_{\text{index}}\) is the lengthscale hyperparameter, \(\nu\) is the smoothness parameter, \(\Gamma\) is the Gamma function, and \(K_\nu\) is the modified Bessel function of the second kind.

Implementation Algorithm

1. Computes distance \(d\) and scaling parameter \(r = \frac{\sqrt{2\nu}d}{\ell}\).
2. Evaluates the term using std::tgamma and Boost's boost::math::cyl_bessel_k implementation of the modified Bessel function.
3. Evaluates analytical derivatives with respect to the lengthscale \(\ell\).

Constructor & Destructor Documentation

Matern() [1/3]

cmp::covariance::Matern::Matern ( const Matern &  )

default

Matern() [2/3]

cmp::covariance::Matern::Matern ( Matern &&  )

default

Matern() [3/3]

cmp::covariance::Matern::Matern ( const size_t &  index, const double &  nu, const int &  indexX = -1  )

inline

Member Function Documentation

eval()

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

inlinevirtual

Implements cmp::covariance::Covariance.

evalGradient()

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

inlinestatic

operator=() [1/2]

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

default

operator=() [2/2]

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

default

Member Data Documentation

index_

size_t cmp::covariance::Matern::index_

private

Hyperparameter index for the lengthscale parameter.

indexX_

int cmp::covariance::Matern::indexX_

private

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

nu_

double cmp::covariance::Matern::nu_

private

Smoothness parameter nu.

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

• include/covariance.h