BFGS storage. More...

#include <BFGSStorage.hpp>

Public Member Functions
	BFGSStorage (Eigen::Index n, Eigen::Index, Scalar, OutputFunction &output_function)
	Construct a BFGS storage. More...

void	reset ()
	Reset the (inverse) Hessian approximation to identity matrix. More...

Vector< Scalar >	calculate_Hv (const Vector< Scalar > &v)
	Calculate product of inverse Hessian approximation $\mathbf{H}$ with vector $\mathbf{v}$ . More...

Scalar	calculate_vHv (const Vector< Scalar > &v)
	Calculate normalized scalar product of vector $\mathbf{v}$ with inverse Hessian approximation $\mathbf{H}$ . More...

const Matrix< Scalar > &	calculate_H ()
	Access the inverse Hessian approximation $\mathbf{H}$ . More...

Vector< Scalar >	calculate_Bv (const Vector< Scalar > &v)
	Calculate product of Hessian approximation $\mathbf{B}$ with vector $\mathbf{v}$ . More...

Scalar	calculate_vBv (const Vector< Scalar > &v)
	Calculate normalized scalar product of vector $\mathbf{v}$ with Hessian approximation $\mathbf{B}$ . More...

const Matrix< Scalar > &	calculate_B ()
	Access the Hessian approximation $\mathbf{B}$ . More...

bool	update (const Vector< Scalar > &s, const Vector< Scalar > &y, const Vector< Scalar > &g)
	Update the (inverse) Hessian approximation. More...

Public Attributes
Eigen::Index	n
	dimensionality of the problem

Matrix< Scalar >	H
	inverse Hessian approximation

Matrix< Scalar >	B
	Hessian approximation.

bool	initial
	is this the initial approximation?

OutputFunction &	output_function
	output function for status messages

Detailed Description

template<typename Scalar, typename OutputFunction>
struct LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >

BFGS storage.

This is the implementation of the BFGS algorithm. It directly stores the approximate Hessian $\mathbf{B}$ and the inverse approximate inverse Hessian $\mathbf{H}$ .

Template Parameters

Scalar The scalar type of vector/matrix coefficients.

It requires $\Theta(n^2)$ storage!

Constructor & Destructor Documentation

◆ BFGSStorage()

template<typename Scalar , typename OutputFunction >

LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::BFGSStorage	(	Eigen::Index	n,
		Eigen::Index	,
		Scalar	,
		OutputFunction &	output_function
	)

Construct a BFGS storage.

Parameters

n	Dimensionality of the problem.
output_function	Output function for status messages.

The second and third parameter are unused.

Member Function Documentation

◆ calculate_B()

template<typename Scalar , typename OutputFunction >

const Matrix< Scalar > & LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::calculate_B ( )

Access the Hessian approximation $\mathbf{B}$ .

Runtime $\Theta(1)$ .

◆ calculate_Bv()

template<typename Scalar , typename OutputFunction >

Vector< Scalar > LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::calculate_Bv ( const Vector< Scalar > & v )

Calculate product of Hessian approximation $\mathbf{B}$ with vector $\mathbf{v}$ .

Parameters

v	Vector $\mathbf{v}$ for calculation.

Returns: The product $\mathbf{B} \mathbf{v}$ .

Runtime $\Theta(n^2)$ .

◆ calculate_H()

template<typename Scalar , typename OutputFunction >

const Matrix< Scalar > & LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::calculate_H ( )

Access the inverse Hessian approximation $\mathbf{H}$ .

Runtime $\Theta(1)$ .

◆ calculate_Hv()

template<typename Scalar , typename OutputFunction >

Vector< Scalar > LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::calculate_Hv ( const Vector< Scalar > & v )

Calculate product of inverse Hessian approximation $\mathbf{H}$ with vector $\mathbf{v}$ .

Parameters

v	Vector $\mathbf{v}$ for calculation.

Returns: The product $\mathbf{H} \mathbf{v}$ .

Runtime $\Theta(n^2)$ .

◆ calculate_vBv()

template<typename Scalar , typename OutputFunction >

Scalar LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::calculate_vBv ( const Vector< Scalar > & v )

Calculate normalized scalar product of vector $\mathbf{v}$ with Hessian approximation $\mathbf{B}$ .

Parameters

v	Vector $\mathbf{v}$ for calculation.

Returns: The normalized scalar product $\mathbf{v}^\intercal \mathbf{B} \mathbf{v}$ .

Runtime $\Theta(n^2)$ .

◆ calculate_vHv()

template<typename Scalar , typename OutputFunction >

Scalar LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::calculate_vHv ( const Vector< Scalar > & v )

Calculate normalized scalar product of vector $\mathbf{v}$ with inverse Hessian approximation $\mathbf{H}$ .

Parameters

v	Vector $\mathbf{v}$ for calculation.

Returns: The normalized scalar product $\mathbf{v}^\intercal \mathbf{H} \mathbf{v}$ .

Runtime $\Theta(n^2)$ .

◆ reset()

template<typename Scalar , typename OutputFunction >

void LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::reset ( )

Reset the (inverse) Hessian approximation to identity matrix.

Runtime $\Theta(n^2)$ .

◆ update()

template<typename Scalar , typename OutputFunction >

bool LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >::update	(	const Vector< Scalar > &	s,
		const Vector< Scalar > &	y,
		const Vector< Scalar > &	g
	)

Update the (inverse) Hessian approximation.

Parameters

s	Change in x coordinate.
y	Change in gradient.
g	New gradient.

Returns: true if successful, false otherwise

Runtime $\omega(n^2)$ (depends on the matrix multiplication algorithm in Eigen).

Todo:: Here we could also introduce a check if the product B * H really is the identity.

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

include/LSLOpt/Implementation/BFGSStorage.hpp

Public Member Functions

Public Attributes

Detailed Description

template<typename Scalar, typename OutputFunction> struct LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >

Constructor & Destructor Documentation

◆ BFGSStorage()

Member Function Documentation

◆ calculate_B()

◆ calculate_Bv()

◆ calculate_H()

◆ calculate_Hv()

◆ calculate_vBv()

◆ calculate_vHv()

◆ reset()

◆ update()

template<typename Scalar, typename OutputFunction>
struct LSLOpt::Implementation::BFGSStorage< Scalar, OutputFunction >