cmp::kernel::IsotropicBandwidth Class Reference

Isotropic bandwidth matrix (single scalar parameter h). More...

#include <kernel++.h>

Inheritance diagram for cmp::kernel::IsotropicBandwidth:

Collaboration diagram for cmp::kernel::IsotropicBandwidth:

Public Member Functions
	IsotropicBandwidth ()=delete
	IsotropicBandwidth (const double &h, const size_t &dim)
	Constructs an IsotropicBandwidth object.
Eigen::VectorXd	apply (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2) const override
	Scales the distance between two vectors by 1/h.
double	determinant () const override
	Computes the determinant of the bandwidth matrix (h^D).
size_t	size () const override
	Returns the dimension of the space.
Eigen::VectorXd	gradientOfApply (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2, const size_t &i) const override
	Computes the gradient of the scaling transformation with respect to h.
double	gradientOfLogDeterminant (const size_t &i) const override
	Computes the gradient of the log-determinant (D / h).
void	setFromVector (const Eigen::VectorXd &params)
	Sets the bandwidth parameter from a parameter vector.
Eigen::VectorXd	getParams () const
	Returns the bandwidth parameter vector.
Public Member Functions inherited from cmp::kernel::Bandwidth
virtual	~Bandwidth ()=default

Static Public Member Functions
static std::shared_ptr< Bandwidth >	make (const double &h, const size_t &dim)
	Factory method for creating an IsotropicBandwidth.

Private Attributes
double	h_ {1.0}
	Bandwidth scalar parameter.
size_t	dim_ {1}
	Dimension of the input data.

Detailed Description

Isotropic bandwidth matrix (single scalar parameter h).

Mathematical Formulation Defines a spherical scaling matrix \(\mathbf{H} = h \mathbf{I}_D\). The transformation scales inputs uniformly:

\[ \mathbf{z} = \frac{1}{h} (\mathbf{x}_1 - \mathbf{x}_2) \]

The determinant is \(\det(\mathbf{H}) = h^D\).

Constructor & Destructor Documentation

IsotropicBandwidth() [1/2]

cmp::kernel::IsotropicBandwidth::IsotropicBandwidth ( )

delete

IsotropicBandwidth() [2/2]

cmp::kernel::IsotropicBandwidth::IsotropicBandwidth ( const double &  h, const size_t &  dim  )

inline

Constructs an IsotropicBandwidth object.

Parameters

h	Smoothing bandwidth scalar.
dim	Dimension of the data.

Member Function Documentation

apply()

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

overridevirtual

Scales the distance between two vectors by 1/h.

Implements cmp::kernel::Bandwidth.

determinant()

double cmp::kernel::IsotropicBandwidth::determinant ( ) const

overridevirtual

Computes the determinant of the bandwidth matrix (h^D).

Implements cmp::kernel::Bandwidth.

getParams()

Eigen::VectorXd cmp::kernel::IsotropicBandwidth::getParams ( ) const

inlinevirtual

Returns the bandwidth parameter vector.

Implements cmp::kernel::Bandwidth.

gradientOfApply()

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

overridevirtual

Computes the gradient of the scaling transformation with respect to h.

Implements cmp::kernel::Bandwidth.

gradientOfLogDeterminant()

double cmp::kernel::IsotropicBandwidth::gradientOfLogDeterminant ( const size_t &  i ) const

overridevirtual

Computes the gradient of the log-determinant (D / h).

Implements cmp::kernel::Bandwidth.

make()

static std::shared_ptr< Bandwidth > cmp::kernel::IsotropicBandwidth::make ( const double &  h, const size_t &  dim  )

inlinestatic

Factory method for creating an IsotropicBandwidth.

setFromVector()

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

inlinevirtual

Sets the bandwidth parameter from a parameter vector.

Implements cmp::kernel::Bandwidth.

size()

size_t cmp::kernel::IsotropicBandwidth::size ( ) const

inlineoverridevirtual

Returns the dimension of the space.

Implements cmp::kernel::Bandwidth.

Member Data Documentation

dim_

size_t cmp::kernel::IsotropicBandwidth::dim_ {1}

private

Dimension of the input data.

h_

double cmp::kernel::IsotropicBandwidth::h_ {1.0}

private

Bandwidth scalar parameter.

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

• include/kernel++.h
• src/kernel++.cpp