#include <alpaqa/accelerators/anderson.hpp>

Detailed Description

template<Config Conf = DefaultConfig>
class alpaqa::AndersonAccel< Conf >

Anderson Acceleration.

Algorithm for accelerating fixed-point iterations for finding fixed points of a function $g$ , i.e. $g (x^{⋆}) = x^{⋆}$ , or equivalently, roots of the residual $r (x) ≜ g (x) - x$ .

Definition at line 39 of file anderson.hpp.

Collaboration diagram for AndersonAccel< Conf >:

Public Types
using	Params = AndersonAccelParams< config_t >

Public Member Functions
	AndersonAccel ()=default

	AndersonAccel (Params params)

	AndersonAccel (Params params, length_t n)

void	resize (length_t n)
	Change the problem dimension.

void	initialize (crvec g_0, crvec r_0)
	Call this function on the first iteration to initialize the accelerator.

void	compute (crvec gₖ, crvec rₖ, rvec xₖ_aa)
	Compute the accelerated iterate $x_{AA}^{k}$ , given the function value at the current iterate $g^{k} = g (x^{k})$ and the corresponding residual $r^{k} = g^{k} - x^{k}$ .

void	compute (crvec gₖ, vec &&rₖ, rvec xₖ_aa)
	Compute the accelerated iterate $x_{AA}^{k}$ , given the function value at the current iterate $g^{k} = g (x^{k})$ and the corresponding residual $r^{k} = g^{k} - x^{k}$ .

void	reset ()
	Reset the accelerator (but keep the last function value and residual, so calling initialize is not necessary).

length_t	n () const
	Get the problem dimension.

length_t	history () const
	Get the maximum number of stored columns.

length_t	current_history () const
	Get the number of columns currently stored in the buffer.

const Params &	get_params () const
	Get the parameters.

std::string	get_name () const

void	scale_R (real_t scal)
	Scale the factorization.

const LimitedMemoryQR< config_t > &	get_QR () const
	For testing purposes.

Private Attributes
Params	params

LimitedMemoryQR< config_t >	qr

mat	G

vec	rₗₐₛₜ

vec	γ_LS

bool	initialized = false

Member Typedef Documentation

◆ Params

template<Config Conf = DefaultConfig>

using Params = AndersonAccelParams<config_t>

Definition at line 42 of file anderson.hpp.

Constructor & Destructor Documentation

◆ AndersonAccel() [1/3]

template<Config Conf = DefaultConfig>

AndersonAccel ( )

default

◆ AndersonAccel() [2/3]

template<Config Conf = DefaultConfig>

AndersonAccel ( Params params )

inline

Parameters

params Parameters.

Definition at line 47 of file anderson.hpp.

◆ AndersonAccel() [3/3]

template<Config Conf = DefaultConfig>

AndersonAccel	(	Params	params,
		length_t	n
	)

inline

Parameters

params	Parameters.
n	Problem dimension (size of the vectors).

Definition at line 52 of file anderson.hpp.

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Member Function Documentation

◆ resize()

template<Config Conf = DefaultConfig>

void resize ( length_t n )

inline

Change the problem dimension.

Flushes the history.

Parameters

n	Problem dimension (size of the vectors).

Definition at line 57 of file anderson.hpp.

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◆ initialize()

template<Config Conf = DefaultConfig>

void initialize	(	crvec	g_0,
		crvec	r_0
	)

inline

Call this function on the first iteration to initialize the accelerator.

Definition at line 67 of file anderson.hpp.

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◆ compute() [1/2]

template<Config Conf = DefaultConfig>

void compute	(	crvec	gₖ,
		crvec	rₖ,
		rvec	xₖ_aa
	)

inline

Compute the accelerated iterate $x_{AA}^{k}$ , given the function value at the current iterate $g^{k} = g (x^{k})$ and the corresponding residual $r^{k} = g^{k} - x^{k}$ .

Definition at line 79 of file anderson.hpp.

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◆ compute() [2/2]

template<Config Conf = DefaultConfig>

void compute	(	crvec	gₖ,
		vec &&	rₖ,
		rvec	xₖ_aa
	)

inline

Compute the accelerated iterate $x_{AA}^{k}$ , given the function value at the current iterate $g^{k} = g (x^{k})$ and the corresponding residual $r^{k} = g^{k} - x^{k}$ .

Definition at line 89 of file anderson.hpp.

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◆ reset()

template<Config Conf = DefaultConfig>

void reset ( )

inline

Reset the accelerator (but keep the last function value and residual, so calling initialize is not necessary).

Definition at line 101 of file anderson.hpp.

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◆ n()

template<Config Conf = DefaultConfig>

length_t n ( ) const

inline

Get the problem dimension.

Definition at line 109 of file anderson.hpp.

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◆ history()

template<Config Conf = DefaultConfig>

length_t history ( ) const

inline

Get the maximum number of stored columns.

Definition at line 111 of file anderson.hpp.

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◆ current_history()

template<Config Conf = DefaultConfig>

length_t current_history ( ) const

inline

Get the number of columns currently stored in the buffer.

Definition at line 113 of file anderson.hpp.

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◆ get_params()

template<Config Conf = DefaultConfig>

const Params & get_params ( ) const

inline

Get the parameters.

Definition at line 116 of file anderson.hpp.

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◆ get_name()

template<Config Conf = DefaultConfig>

std::string get_name ( ) const

inline

Definition at line 118 of file anderson.hpp.

◆ scale_R()

template<Config Conf = DefaultConfig>

void scale_R ( real_t scal )

inline

Scale the factorization.

Definition at line 123 of file anderson.hpp.

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◆ get_QR()

template<Config Conf = DefaultConfig>

const LimitedMemoryQR< config_t > & get_QR ( ) const

inline

For testing purposes.

Definition at line 126 of file anderson.hpp.

Member Data Documentation

◆ params

template<Config Conf = DefaultConfig>

Params params

private

Definition at line 129 of file anderson.hpp.

◆ qr

template<Config Conf = DefaultConfig>

LimitedMemoryQR<config_t> qr

private

Definition at line 130 of file anderson.hpp.

◆ G

template<Config Conf = DefaultConfig>

mat G

private

Definition at line 131 of file anderson.hpp.

◆ rₗₐₛₜ

template<Config Conf = DefaultConfig>

vec rₗₐₛₜ

private

Definition at line 132 of file anderson.hpp.

◆ γ_LS

template<Config Conf = DefaultConfig>

vec γ_LS

private

Definition at line 133 of file anderson.hpp.

◆ initialized

template<Config Conf = DefaultConfig>

bool initialized = false

private

Definition at line 134 of file anderson.hpp.

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

src/alpaqa/include/alpaqa/accelerators/anderson.hpp

Detailed Description

Public Types

Public Member Functions

Private Attributes

Member Typedef Documentation

◆ Params

Constructor & Destructor Documentation

◆ AndersonAccel() [1/3]

◆ AndersonAccel() [2/3]

◆ AndersonAccel() [3/3]

Member Function Documentation

◆ resize()

◆ initialize()

◆ compute() [1/2]

◆ compute() [2/2]

◆ reset()

◆ n()

◆ history()

◆ current_history()

◆ get_params()

◆ get_name()

◆ scale_R()

◆ get_QR()

Member Data Documentation

◆ params

◆ qr

◆ G

◆ rₗₐₛₜ

◆ γ_LS

◆ initialized