AndersonAccel< Conf > Class Template Reference

#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. \( g(x^\star) = x^\star \), or equivalently, roots of the residual \( r(x) \triangleq g(x) - x \).

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 \( x^k_\text{AA} \), 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 \( x^k_\text{AA} \), 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.

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.

compute() [1/2]

template<Config Conf = DefaultConfig>

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

inline

Compute the accelerated iterate \( x^k_\text{AA} \), 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.

compute() [2/2]

template<Config Conf = DefaultConfig>

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

inline

Compute the accelerated iterate \( x^k_\text{AA} \), 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.

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.

n()

template<Config Conf = DefaultConfig>

length_t n ( ) const

inline

Get the problem dimension.

Definition at line 109 of file anderson.hpp.

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.

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.

get_params()

template<Config Conf = DefaultConfig>

const Params & get_params ( ) const

inline

Get the parameters.

Definition at line 116 of file anderson.hpp.

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.

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.

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

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