cmp::kernel::Bandwidth Class Reference

Abstract base class for multivariate KDE bandwidth matrices. More...

#include <kernel++.h>

Inheritance diagram for cmp::kernel::Bandwidth:

Public Member Functions
virtual	~Bandwidth ()=default
virtual Eigen::VectorXd	apply (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2) const =0
virtual double	determinant () const =0
virtual size_t	size () const =0
virtual Eigen::VectorXd	gradientOfApply (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2, const size_t &i) const =0
virtual double	gradientOfLogDeterminant (const size_t &i) const =0
virtual void	setFromVector (const Eigen::VectorXd &params)=0
virtual Eigen::VectorXd	getParams () const =0

Detailed Description

Abstract base class for multivariate KDE bandwidth matrices.

Mathematical Formulation The bandwidth matrix \(\mathbf{H} \in \mathbb{R}^{D \times D}\) acts as a linear transformation scaling spatial distances:

\[ \mathbf{z} = \mathbf{H}^{-1} (\mathbf{x}_1 - \mathbf{x}_2) \]

The smoothing kernel scales inversely with the determinant: \(\frac{1}{\det(\mathbf{H})}\).

Implementation Algorithm Defines virtual methods to compute coordinate scaling (apply), matrix determinant (determinant), and parameter gradients for NLopt optimization.

Constructor & Destructor Documentation

~Bandwidth()

virtual cmp::kernel::Bandwidth::~Bandwidth ( )

virtualdefault

Member Function Documentation

apply()

virtual Eigen::VectorXd cmp::kernel::Bandwidth::apply ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2  ) const

pure virtual

Implemented in cmp::kernel::IsotropicBandwidth, cmp::kernel::DiagonalBandwidth, and cmp::kernel::FullBandwidth.

determinant()

virtual double cmp::kernel::Bandwidth::determinant ( ) const

pure virtual

Implemented in cmp::kernel::IsotropicBandwidth, cmp::kernel::DiagonalBandwidth, and cmp::kernel::FullBandwidth.

getParams()

virtual Eigen::VectorXd cmp::kernel::Bandwidth::getParams ( ) const

pure virtual

Implemented in cmp::kernel::IsotropicBandwidth, cmp::kernel::DiagonalBandwidth, and cmp::kernel::FullBandwidth.

gradientOfApply()

virtual Eigen::VectorXd cmp::kernel::Bandwidth::gradientOfApply ( const Eigen::VectorXd &  x1, const Eigen::VectorXd &  x2, const size_t &  i  ) const

pure virtual

Implemented in cmp::kernel::IsotropicBandwidth, cmp::kernel::DiagonalBandwidth, and cmp::kernel::FullBandwidth.

gradientOfLogDeterminant()

virtual double cmp::kernel::Bandwidth::gradientOfLogDeterminant ( const size_t &  i ) const

pure virtual

Implemented in cmp::kernel::IsotropicBandwidth, cmp::kernel::DiagonalBandwidth, and cmp::kernel::FullBandwidth.

setFromVector()

virtual void cmp::kernel::Bandwidth::setFromVector ( const Eigen::VectorXd &  params )

pure virtual

Implemented in cmp::kernel::IsotropicBandwidth, cmp::kernel::DiagonalBandwidth, and cmp::kernel::FullBandwidth.

size()

virtual size_t cmp::kernel::Bandwidth::size ( ) const

pure virtual

Implemented in cmp::kernel::FullBandwidth, cmp::kernel::IsotropicBandwidth, and cmp::kernel::DiagonalBandwidth.

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

• include/kernel++.h