ModuleBase::Opt_CG Class Reference

A class designed to deal with optimization problems with CG method. Three forms of CG methods have been implemented, including standard flow to solve the linear equation Ax = b, Polak-Ribire (PR) form and Hager-Zhang (HZ) form to solve general optimization problems min{f(x)}. We adopt following abbreviation x -> solution d -> direction g -> gradient. More...

#include <opt_CG.h>

Collaboration diagram for ModuleBase::Opt_CG:

Public Member Functions
	Opt_CG ()
	~Opt_CG ()
void	init_b (double *pinp_b)
	Initialize b before solving Ax = b.
void	allocate (int nx)
	Allocate the space for pdirect_old and pgradient_old.
void	set_para (double dV)
void	refresh (int nx_new=0, double *pinp_b=nullptr)
	Refresh the class. If nx changes, reallocate space. If b is provided, initialize it.
void	next_direct (double *pgradient, int label, double *rdirect)
	Get the next optimization direction.
double	step_length (double *pAd, double *pdirect, int &ifPD)
	Get the step length, only work for standard CG.
double	get_residual ()
int	get_iter ()

Private Member Functions
void	stantard_CGdirect (double *pAd, double *rdirect)
	Get the next optimization direction with standard CG workflow.
void	PR_beta (double *pgradient)
	Get the beta in PR form. beta_k = max{0, <g_k, g_k-g_{k-1}>/<g_{k-1}, g_{k-1}>} <> means inner product.
void	HZ_beta (double *pgradient)
	Get the beta in HZ form. See formula in Hager W W, Zhang H. SIAM Journal on optimization, 2005, 16(1): 170-192.
double	inner_product (double *pa, double *pb, int length)

Private Attributes
double	dV_ = 1.
int	nx_ = 0
int	iter_ = 0
double	gg_ = 1000
double	beta_ = 0.
double	eta_ = 0.01
double *	pdirect_old_ = nullptr
double *	pgradient_old_ = nullptr
double	alpha_ = 0.
double *	pb_ = nullptr

Detailed Description

A class designed to deal with optimization problems with CG method. Three forms of CG methods have been implemented, including standard flow to solve the linear equation Ax = b, Polak-Ribire (PR) form and Hager-Zhang (HZ) form to solve general optimization problems min{f(x)}. We adopt following abbreviation x -> solution d -> direction g -> gradient.

Author

sunliang

Constructor & Destructor Documentation

Opt_CG()

ModuleBase::Opt_CG::Opt_CG

(

)

~Opt_CG()

ModuleBase::Opt_CG::~Opt_CG

(

)

Member Function Documentation

allocate()

void ModuleBase::Opt_CG::allocate

(

int

nx

)

Allocate the space for pdirect_old and pgradient_old.

Parameters

nx	length of the solution array x

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get_iter()

int ModuleBase::Opt_CG::get_iter ( )

inline

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get_residual()

double ModuleBase::Opt_CG::get_residual ( )

inline

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HZ_beta()

void ModuleBase::Opt_CG::HZ_beta ( double *  pgradient )

private

Get the beta in HZ form. See formula in Hager W W, Zhang H. SIAM Journal on optimization, 2005, 16(1): 170-192.

Parameters

pgradient

df(x)/dx

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init_b()

void ModuleBase::Opt_CG::init_b

(

double *

pinp_b

)

Initialize b before solving Ax = b.

Parameters

pinp_b

b in the linear equation Ax = b

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inner_product()

double ModuleBase::Opt_CG::inner_product ( double *  pa, double *  pb, int  length  )

inlineprivate

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next_direct()

void ModuleBase::Opt_CG::next_direct	(	double *	pgradient,
		int	label,
		double *	rdirect
	)

Get the next optimization direction.

Parameters

[in]	pgradient	Ad for linear equaiont Ax=b, and gradient for general case
[in]	label	0 for solve Ax=b, 1 for PR form, 2 for HZ form.
[in,out]	rdirect	the next optimization direction

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PR_beta()

void ModuleBase::Opt_CG::PR_beta ( double *  pgradient )

private

Get the beta in PR form. beta_k = max{0, <g_k, g_k-g_{k-1}>/<g_{k-1}, g_{k-1}>} <> means inner product.

Parameters

pgradient

df(x)/dx

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refresh()

void ModuleBase::Opt_CG::refresh	(	int	nx_new = 0,
		double *	pinp_b = nullptr
	)

Refresh the class. If nx changes, reallocate space. If b is provided, initialize it.

Parameters

nx_new	length of new x, default 0 means the length doesn't change
pinp_b	new b in Ax = b, default nullptr means we are dealing with general case

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set_para()

void ModuleBase::Opt_CG::set_para

(

double

dV

)

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stantard_CGdirect()

void ModuleBase::Opt_CG::stantard_CGdirect ( double *  pAd, double *  rdirect  )

private

Get the next optimization direction with standard CG workflow.

Parameters

[in]	pAd	Ad for Ax=b
[out]	rdirect	the next direction

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step_length()

double ModuleBase::Opt_CG::step_length	(	double *	pAd,
		double *	pdirect,
		int &	ifPD
	)

Get the step length, only work for standard CG.

Parameters

pAd	Ad for Ax=b
pdirect	direction
ifPD	0 if positive definite, -1, -2 when not

Returns

the step length alpha

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Member Data Documentation

alpha_

double ModuleBase::Opt_CG::alpha_ = 0.

private

beta_

double ModuleBase::Opt_CG::beta_ = 0.

private

dV_

double ModuleBase::Opt_CG::dV_ = 1.

private

eta_

double ModuleBase::Opt_CG::eta_ = 0.01

private

gg_

double ModuleBase::Opt_CG::gg_ = 1000

private

iter_

int ModuleBase::Opt_CG::iter_ = 0

private

nx_

int ModuleBase::Opt_CG::nx_ = 0

private

pb_

double* ModuleBase::Opt_CG::pb_ = nullptr

private

pdirect_old_

double* ModuleBase::Opt_CG::pdirect_old_ = nullptr

private

pgradient_old_

double* ModuleBase::Opt_CG::pgradient_old_ = nullptr

private

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

• /home/runner/work/abacus-develop/abacus-develop/source/source_base/opt_CG.h
• /home/runner/work/abacus-develop/abacus-develop/source/source_base/opt_CG.cpp