AndersonAccel Class Reference

#include <quala/anderson-acceleration.hpp>

Detailed Description

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 \( r(x) \triangleq g(x) - x \).

Todo:

Condition estimation of the QR factorization.

Definition at line 33 of file anderson-acceleration.hpp.

Collaboration diagram for AndersonAccel:

Public Types
using	Params = AndersonAccelParams

Public Member Functions
	AndersonAccel (Params params)
	AndersonAccel (Params params, length_t n)
void	resize (length_t n)
	Change the problem dimension. More...
void	initialize (crvec g_0, vec r_0)
	Call this function on the first iteration to initialize the accelerator. More...
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 \( r^k = g^k - x^k \). More...
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 \( r^k = g^k - x^k \). More...
void	reset ()
	Reset the accelerator (but keep the last function value and residual, so calling initialize is not necessary). More...
length_t	n () const
	Get the problem dimension. More...
length_t	history () const
	Get the maximum number of stored columns. More...
length_t	current_history () const
	Get the number of columns currently stored in the buffer. More...
const Params &	get_params () const
	Get the parameters. More...

Private Attributes
Params	params
LimitedMemoryQR	qr
mat	G
vec	rₗₐₛₜ
vec	γ_LS
bool	initialized = false

Member Typedef Documentation

Params

using Params = AndersonAccelParams

Definition at line 35 of file anderson-acceleration.hpp.

Constructor & Destructor Documentation

AndersonAccel() [1/2]

AndersonAccel ( Params  params )

inline

Parameters

params

Parameters.

Definition at line 39 of file anderson-acceleration.hpp.

AndersonAccel() [2/2]

AndersonAccel ( Params  params, length_t  n  )

inline

Parameters

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

Definition at line 44 of file anderson-acceleration.hpp.

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Member Function Documentation

resize()

void resize ( length_t  n )

inline

Change the problem dimension.

Flushes the history.

Parameters

n	Problem dimension (size of the vectors).

Definition at line 49 of file anderson-acceleration.hpp.

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initialize()

void initialize ( crvec  g_0, vec  r_0  )

inline

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

Definition at line 59 of file anderson-acceleration.hpp.

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compute() [1/2]

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 71 of file anderson-acceleration.hpp.

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compute() [2/2]

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 81 of file anderson-acceleration.hpp.

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reset()

void reset ( )

inline

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

Definition at line 93 of file anderson-acceleration.hpp.

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n()

length_t n ( ) const

inline

Get the problem dimension.

Definition at line 101 of file anderson-acceleration.hpp.

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history()

length_t history ( ) const

inline

Get the maximum number of stored columns.

Definition at line 103 of file anderson-acceleration.hpp.

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current_history()

length_t current_history ( ) const

inline

Get the number of columns currently stored in the buffer.

Definition at line 105 of file anderson-acceleration.hpp.

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get_params()

const Params & get_params ( ) const

inline

Get the parameters.

Definition at line 108 of file anderson-acceleration.hpp.

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Member Data Documentation

params

Params params

private

Definition at line 111 of file anderson-acceleration.hpp.

qr

LimitedMemoryQR qr

private

Definition at line 112 of file anderson-acceleration.hpp.

G

mat G

private

Definition at line 113 of file anderson-acceleration.hpp.

rₗₐₛₜ

vec rₗₐₛₜ

private

Definition at line 114 of file anderson-acceleration.hpp.

γ_LS

vec γ_LS

private

Definition at line 115 of file anderson-acceleration.hpp.

initialized

bool initialized = false

private

Definition at line 116 of file anderson-acceleration.hpp.

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

• anderson-acceleration.hpp