#include <anderson_mixer.hpp>

Inherits sirius::mixer::Mixer< FUNCS... >.

Public Member Functions
	Anderson (std::size_t max_history, double beta, double beta0, double beta_scaling_factor)

void	mix_impl () override

Public Member Functions inherited from sirius::mixer::Mixer< FUNCS... >
	Mixer (std::size_t max_history)
	Construct a mixer. Functions have to initialized individually. More...

void	initialize_function (const FunctionProperties< typename std::tuple_element< FUNC_INDEX, std::tuple< FUNCS... > >::type > &function_prop, const typename std::tuple_element< FUNC_INDEX, std::tuple< FUNCS... > >::type &init_value, ARGS &&... args)

void	set_input (const typename std::tuple_element< FUNC_INDEX, std::tuple< FUNCS... > >::type &input)
	Set input for next mixing step. More...

void	get_output (typename std::tuple_element< FUNC_INDEX, std::tuple< FUNCS... > >::type &output)
	Access last generated output. Mixing must have been performed at least once. More...

double	mix (double rms_min__)
	Mix input and stored history. Returns the root mean square error computed by inner products of residuals. More...

Private Attributes
double	beta_

double	beta0_

double	beta_scaling_factor_

sddk::mdarray< double, 2 >	S_

sddk::mdarray< double, 2 >	S_factorized_

std::size_t	history_size_

Additional Inherited Members
Static Public Attributes inherited from sirius::mixer::Mixer< FUNCS... >
static constexpr std::size_t	number_of_functions

Protected Member Functions inherited from sirius::mixer::Mixer< FUNCS... >
virtual void	mix_impl ()=0

void	update_residual ()

void	update_rms ()

std::size_t	idx_hist (std::size_t step) const

double	inner_product (const std::tuple< std::unique_ptr< FUNCS >... > &x, const std::tuple< std::unique_ptr< FUNCS >... > &y)

void	scale (double alpha, std::tuple< std::unique_ptr< FUNCS >... > &x)

void	copy (const std::tuple< std::unique_ptr< FUNCS >... > &x, std::tuple< std::unique_ptr< FUNCS >... > &y)

void	axpy (double alpha, const std::tuple< std::unique_ptr< FUNCS >... > &x, std::tuple< std::unique_ptr< FUNCS >... > &y)

void	rotate (double c, double s, std::tuple< std::unique_ptr< FUNCS >... > &x, std::tuple< std::unique_ptr< FUNCS >... > &y)

Protected Attributes inherited from sirius::mixer::Mixer< FUNCS... >
std::size_t	step_

std::size_t	max_history_

std::vector< double >	rmse_history_

std::tuple< FunctionProperties< FUNCS >... >	functions_

std::tuple< std::unique_ptr< FUNCS >... >	input_

std::vector< std::tuple< std::unique_ptr< FUNCS >... > >	output_history_

std::vector< std::tuple< std::unique_ptr< FUNCS >... > >	residual_history_

Detailed Description

template<typename... FUNCS>
class sirius::mixer::Anderson< FUNCS >

Anderson mixer.

Quasi-Newton limited-memory method which updates \( x_{n+1} = x_n - G_nf_n \) where \( G_n \) is an approximate inverse Jacobian. Anderson is derived by taking the low-rank update to the inverse Jacobian

\[ G_{n+1} = (G_n + \Delta X_n - G_n \Delta F_n)(\Delta F_n^T \Delta F_n)^{-1}\Delta F_n^T \]

such that the secant equations \( G_{n+1} \Delta F_n = \Delta X_n \) are satisfied for previous iterations. Then \( G_n \) is taken \( -\beta I \). The Anderson class explicitly constructs the Gram matrix \( \Delta F_n^T \Delta F_n \) to solve the least-squares problem. For more stability use Anderson_stable, which comes at the cost of orthogonalizing \( \Delta F_n \).

Reference paper: Fang, Haw‐ren, and Yousef Saad. "Two classes of multisecant methods for nonlinear acceleration." Numerical Linear Algebra with Applications 16.3 (2009): 197-221.

Definition at line 65 of file anderson_mixer.hpp.

Constructor & Destructor Documentation

◆ Anderson()

template<typename... FUNCS>

sirius::mixer::Anderson< FUNCS >::Anderson	(	std::size_t	max_history,
		double	beta,
		double	beta0,
		double	beta_scaling_factor
	)

inline

Definition at line 75 of file anderson_mixer.hpp.

Member Function Documentation

◆ mix_impl()

template<typename... FUNCS>

void sirius::mixer::Anderson< FUNCS >::mix_impl ( )

template<typename... FUNCS>

std::size_t sirius::mixer::Anderson< FUNCS >::history_size_

private

Definition at line 73 of file anderson_mixer.hpp.

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

anderson_mixer.hpp

Public Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Anderson()

Member Function Documentation

◆ mix_impl()

Member Data Documentation

◆ beta_

◆ beta0_

◆ beta_scaling_factor_

◆ S_

◆ S_factorized_

◆ history_size_