#include <BALL/MOLMEC/MINIMIZATION/lineSearch.h>

Public Member Functions
Constructors and Destructors
	LineSearch ()

	LineSearch (EnergyMinimizer &minimizer)

	LineSearch (const LineSearch &line_search)

virtual	~LineSearch ()

Assignments
const LineSearch &	operator= (const LineSearch &LineSearch)

Accessors
void	setAlpha (double alpha)

void	setBeta (double beta)

double	getAlpha () const

double	getBeta () const

Size	getMaxSteps () const

void	setMaxSteps (Size steps)

void	setLowerBound (double lbound)

double	getLowerBound () const

void	setXTol (double xtol)

double	getXTol () const

void	setBracketedFlag (bool bracktd)

bool	isBracketed () const

void	setMinimizer (EnergyMinimizer &minimizer)

virtual void	takeStep (double &st_a, double &f_a, double &g_a, double &st_b, double &f_b, double &g_b, double &stp, double f, double g, double minstp, double maxstp)

Minimization
virtual bool	minimize (double &stp, bool keep_gradient=false)

Protected Attributes
double	alpha_

double	beta_

Size	max_steps_

double	lower_energy_bound_

double	stptol_

bool	is_bracketed_

EnergyMinimizer *	minimizer_

Detailed Description

Basic line search class. This method minimizes the energy of a system along a given direction using a two stage algorithm. It is based on cubic and quadratic interpolation methods of Jorge J. More and David J. Thuente. See

[1] J. More and D. Thuente, "Line search algorithms with guaranteed sufficient decrease," ACM Transactions on Mathematical Software 20 (1994), no. 3, pp. 286-307.

Definition at line 32 of file lineSearch.h.

Constructor & Destructor Documentation

BALL::LineSearch::LineSearch ( )

Default constructor.

BALL::LineSearch::LineSearch ( EnergyMinimizer & minimizer )

Detailed constructor.

BALL::LineSearch::LineSearch ( const LineSearch & line_search )

Copy constructor

virtual BALL::LineSearch::~LineSearch ( )

virtual

Destructor.

Member Function Documentation

double BALL::LineSearch::getAlpha ( ) const

Get the parameter alpha (convergence criterion for the line search).

See also: minimize

double BALL::LineSearch::getBeta ( ) const

Get the parameter beta (convergence criterion for the line search).

See also: minimize

double BALL::LineSearch::getLowerBound ( ) const

Get the lower bound on energy values.

Size BALL::LineSearch::getMaxSteps ( ) const

Get the parameter max_steps.

double BALL::LineSearch::getXTol ( ) const

Get the nonnegative relative tolerance for an acceptable step length.

bool BALL::LineSearch::isBracketed ( ) const

Return whether a minimizer has already been bracketed. Warning: this returns only the flag is_bracketed_. If this flag has not been set by the algorithm but changed by setBracketedFlag this might not be trustworthy!

virtual bool BALL::LineSearch::minimize	(	double &	stp,
		bool	keep_gradient = `false`
	)

virtual

Perform a line search. Find the minimum position for all atoms along the direction provided by the minimization algorithm. A two stage algorithm is used proposed by Jorge J. More and David J. Thuente. If necessary (the convergence criterion is not fulfilled) a minimizer along the given direction is bracketed in the first stage. In the second stage this function looks for a minimizer whithin the bracketed interval. The routine exits

(1) if the strong Wolfe conditions are satisfied (convergence criterion for the line search), that are

$E_{k+1} \leq E_k + \alpha\cdot stp\cdot<g_k, d_k>$

and

$|<g_{k+1}, d_k>| \leq \beta\cdot |<g_k, d_k>|$

where $g_k$ and $g_{k+1}$ are the initial and the current gradient and $d_k$ is the search direction, $E_{k+1}$ is the current and $E_k$ the initial energy (stp = 0), $\alpha$ and $\beta$ are two parameters (usually 0.9 and 0.0001).

(2) if the relative tolerance for an acceptable step is reached (length of the bracketing interval).

(3) if there has been some numerical problems. In this case the best step length which could be found is returned.

Parameters

stp	Unused on entry since the line search always starts with stp = 1.0. On exit the step length corresponding to a successful step or just the best this function was able to find.
keep_gradient	If `true`, we will not calculate the gradient for stp = 1 but assume that this has already been performed instead.

const LineSearch& BALL::LineSearch::operator= ( const LineSearch & LineSearch )

Assignment operator

void BALL::LineSearch::setAlpha ( double alpha )

Set the parameter alpha (convergence criterion for the line search).

See also: minimize

void BALL::LineSearch::setBeta ( double beta )

Set the parameter beta (convergence criterion for the line search).

See also: minimize

void BALL::LineSearch::setBracketedFlag ( bool bracktd )

Set the flag is_bracketed_. The algorithm will act as if a minimizer has already been bracketed (true) or not (false). Warning: this can be useful if a user exactly knows what they are doing. Usually, this flag should not be touched! The algorithm sets this flag automatically if a minimizer could be bracketed.

void BALL::LineSearch::setLowerBound ( double lbound )

Set the lower bound on energy values. An estimation for the maximum step length is computed based on this value.

void BALL::LineSearch::setMaxSteps ( Size steps )

Set the parameter max_steps.

void BALL::LineSearch::setMinimizer ( EnergyMinimizer & minimizer )

Set the minimizer class which provides the search direction and the force field among other things.

void BALL::LineSearch::setXTol ( double xtol )

Set the nonnegative relative tolerance for an acceptable step length.

virtual void BALL::LineSearch::takeStep	(	double &	st_a,
		double &	f_a,
		double &	g_a,
		double &	st_b,
		double &	f_b,
		double &	g_b,
		double &	stp,
		double	f,
		double	g,
		double	minstp,
		double	maxstp
	)

virtual

Computes a safeguarded step for a search procedure by case differentiation dependend on whether a minimum could already be bracketed or not. All computations are done by safeguarded quadratic and cubic interpolation. The interval that contains a step that satisfies a sufficient decrease and the curvature condition is updated. This function is based on the proposed step computation of Jorge J. More and David J. Thuente. Don't worry if interval bounds are changed after this routine exits.

Parameters

st_a	Best step obtained so far and an endpoint of the interval that contains the minimizer.
f_a	Energy value at `st_a`.
g_a	Directional derivative at `st_a`.
st_b	Second endpoint of the interval that contains the minimizer.
f_b	Energy value at `st_b`.
g_b	Directional derivative at `st_b`.
stp	Current step. If `is_bracketed_` is set to `true` then `stp` must be between `st_a` and `st_b`.
f	Energy value at `stp`.
g	Directional derivative at `stp`.
minstp	Lower bound for the step.
maxstp	Upper bound for the step.

Member Data Documentation

double BALL::LineSearch::alpha_

protected

Definition at line 202 of file lineSearch.h.

double BALL::LineSearch::beta_

protected

Definition at line 206 of file lineSearch.h.

bool BALL::LineSearch::is_bracketed_

protected

Definition at line 222 of file lineSearch.h.

double BALL::LineSearch::lower_energy_bound_

protected

Definition at line 214 of file lineSearch.h.

Size BALL::LineSearch::max_steps_

protected

Definition at line 210 of file lineSearch.h.

EnergyMinimizer* BALL::LineSearch::minimizer_

protected

Definition at line 226 of file lineSearch.h.

double BALL::LineSearch::stptol_

protected

Definition at line 218 of file lineSearch.h.

Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation