cmp::kernel::Kernel Class Reference

Abstract base class for KDE density kernel functions. More...

#include <kernel++.h>

Inheritance diagram for cmp::kernel::Kernel:

Public Member Functions
virtual	~Kernel ()=default
virtual double	eval (const Eigen::VectorXd &z) const =0
virtual double	normalizationConstant (const size_t &dim) const =0
virtual double	applyToGradient (const Eigen::VectorXd &z, const Eigen::VectorXd &grad_z_i) const =0

Detailed Description

Abstract base class for KDE density kernel functions.

Mathematical Formulation A multivariate kernel \(K: \mathbb{R}^D \to [0,\infty)\) defines localized weights for smoothing observations, satisfying:

\[ \int_{\mathbb{R}^D} K(\mathbf{z}) d\mathbf{z} = 1.0, \quad \int_{\mathbb{R}^D} \mathbf{z} K(\mathbf{z}) d\mathbf{z} = \mathbf{0} \]

Implementation Algorithm Defines virtual methods for evaluating the kernel value (eval), computing the dimension-dependent normalizing scalar (normalizationConstant), and calculating gradients (applyToGradient).

Constructor & Destructor Documentation

~Kernel()

virtual cmp::kernel::Kernel::~Kernel ( )

virtualdefault

Member Function Documentation

applyToGradient()

virtual double cmp::kernel::Kernel::applyToGradient ( const Eigen::VectorXd &  z, const Eigen::VectorXd &  grad_z_i  ) const

pure virtual

Implemented in cmp::kernel::Gaussian, cmp::kernel::Epanechnikov, and cmp::kernel::Uniform.

eval()

virtual double cmp::kernel::Kernel::eval ( const Eigen::VectorXd &  z ) const

pure virtual

Implemented in cmp::kernel::Gaussian, cmp::kernel::Epanechnikov, and cmp::kernel::Uniform.

normalizationConstant()

virtual double cmp::kernel::Kernel::normalizationConstant ( const size_t &  dim ) const

pure virtual

Implemented in cmp::kernel::Gaussian, cmp::kernel::Epanechnikov, and cmp::kernel::Uniform.

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

• include/kernel++.h