cmp::kernel::FullBandwidth Class Reference

Full covariance bandwidth matrix parameterized by its Cholesky factor. More...

#include <kernel++.h>

Inheritance diagram for cmp::kernel::FullBandwidth:

Collaboration diagram for cmp::kernel::FullBandwidth:

Public Member Functions
	FullBandwidth ()=delete
	FullBandwidth (const Eigen::MatrixXd &LLT)
	Constructs a FullBandwidth from a positive definite scale matrix.
double	determinant () const override
	Computes the determinant of the bandwidth matrix.
size_t	size () const
	Returns the dimension of the space.
std::pair< size_t, size_t >	indexToRowCol (const size_t &i) const
	Maps a flat index to row and column indices of the Cholesky factor.
Eigen::VectorXd	apply (const Eigen::VectorXd &x1, const Eigen::VectorXd &x2) const override
	Projects the distance vector using the inverse of the Cholesky factor L.
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 parameter i.
double	gradientOfLogDeterminant (const size_t &i) const override
	Computes the gradient of the log-determinant.
void	setFromVector (const Eigen::VectorXd &params) override
	Sets the bandwidth parameters from a parameter vector.
Eigen::VectorXd	getParams () const override
	Gets the bandwidth parameters as a vector.
Eigen::MatrixXd	matrix () const
	Returns the full density bandwidth matrix.
Public Member Functions inherited from cmp::kernel::Bandwidth
virtual	~Bandwidth ()=default

Static Public Member Functions
static std::shared_ptr< Bandwidth >	make (const Eigen::MatrixXd &LLT)
	Factory method for creating a FullBandwidth.

Private Attributes
Eigen::LLT< Eigen::MatrixXd >	L_
	LDLT/Cholesky factor of the covariance scaling matrix.
double	det_
	Precomputed determinant of the full bandwidth matrix.
size_t	dim_
	Dimension of the input space.

Detailed Description

Full covariance bandwidth matrix parameterized by its Cholesky factor.

Mathematical Formulation Represents a full bandwidth matrix parameterized via lower triangular Cholesky factor \(\mathbf{L}\) where:

\[ \mathbf{H} = \mathbf{L} \mathbf{L}^T \]

The transformation projects distances as:

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

The determinant is computed from the diagonal elements of the Cholesky factor:

\[ \det(\mathbf{H}) = \prod_{d=1}^D L_{dd}^2 \]

Constructor & Destructor Documentation

FullBandwidth() [1/2]

cmp::kernel::FullBandwidth::FullBandwidth ( )

delete

FullBandwidth() [2/2]

cmp::kernel::FullBandwidth::FullBandwidth ( const Eigen::MatrixXd &  LLT )

inline

Constructs a FullBandwidth from a positive definite scale matrix.

Member Function Documentation

apply()

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

overridevirtual

Projects the distance vector using the inverse of the Cholesky factor L.

Implements cmp::kernel::Bandwidth.

determinant()

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

overridevirtual

Computes the determinant of the bandwidth matrix.

Implements cmp::kernel::Bandwidth.

getParams()

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

overridevirtual

Gets the bandwidth parameters as a vector.

Implements cmp::kernel::Bandwidth.

gradientOfApply()

Eigen::VectorXd cmp::kernel::FullBandwidth::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 parameter i.

Implements cmp::kernel::Bandwidth.

gradientOfLogDeterminant()

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

overridevirtual

Computes the gradient of the log-determinant.

Implements cmp::kernel::Bandwidth.

indexToRowCol()

std::pair< size_t, size_t > cmp::kernel::FullBandwidth::indexToRowCol

(

const size_t &

i

)

const

Maps a flat index to row and column indices of the Cholesky factor.

make()

static std::shared_ptr< Bandwidth > cmp::kernel::FullBandwidth::make ( const Eigen::MatrixXd &  LLT )

inlinestatic

Factory method for creating a FullBandwidth.

matrix()

Eigen::MatrixXd cmp::kernel::FullBandwidth::matrix ( ) const

inline

Returns the full density bandwidth matrix.

setFromVector()

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

overridevirtual

Sets the bandwidth parameters from a parameter vector.

Implements cmp::kernel::Bandwidth.

size()

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

inlinevirtual

Returns the dimension of the space.

Implements cmp::kernel::Bandwidth.

Member Data Documentation

det_

double cmp::kernel::FullBandwidth::det_

private

Precomputed determinant of the full bandwidth matrix.

dim_

size_t cmp::kernel::FullBandwidth::dim_

private

Dimension of the input space.

L_

Eigen::LLT<Eigen::MatrixXd> cmp::kernel::FullBandwidth::L_

private

LDLT/Cholesky factor of the covariance scaling matrix.

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

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