dev.nm.root.univariate.bracketsearch

Class BrentMinimizer.Solution

java.lang.Object

dev.nm.root.univariate.bracketsearch.BracketSearchMinimizer.Solution

dev.nm.root.univariate.bracketsearch.BrentMinimizer.Solution

All Implemented Interfaces:

UnivariateMinimizer.Solution, MinimizationSolution<Double>

Enclosing class:

BrentMinimizer

public class BrentMinimizer.Solution
extends BracketSearchMinimizer.Solution

This is the solution to a Brent's univariate optimization.

Field Summary

Fields inherited from class dev.nm.root.univariate.bracketsearch.BracketSearchMinimizer.Solution

f, fmin, fnext, iter, xl, xmin, xnext, xu

Method Summary

Modifier and Type	Method and Description
protected void	init(double xmin, double fmin) Initializes the algorithm states with initial \(x_{min}\) and \(f_{min}\) before iterations.
protected boolean	isMinFound() the convergence criterion
double	search(double lower, double upper) Search for a minimum within the interval [lower, upper].
double	search(double lower, double initial, double upper) Search for a minimum within the interval [lower, upper].
protected void	updateStates() Update the bracketing interval and the best min found so far.
protected double	xnext() Compute the next best estimate within the bracketing interval.

Methods inherited from class dev.nm.root.univariate.bracketsearch.BracketSearchMinimizer.Solution

isBracketing, minimizer, minimum

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

search

public double search(double lower,
                     double initial,
                     double upper)

Description copied from interface: UnivariateMinimizer.Solution

Search for a minimum within the interval [lower, upper].

Specified by:

search in interface UnivariateMinimizer.Solution

Overrides:

search in class BracketSearchMinimizer.Solution

Parameters:

lower - the lower bound for the bracketing interval which contains a minimum

initial - an initial guess

upper - the upper bound for the bracketing interval which contains a minimum

Returns:

an approximate minimizer

search

public double search(double lower,
                     double upper)

Description copied from interface: UnivariateMinimizer.Solution

Search for a minimum within the interval [lower, upper].

Parameters:

lower - the lower bound for the bracketing interval which contains a minimum

upper - the upper bound for the bracketing interval which contains a minimum

Returns:

an approximate minimizer

init

protected void init(double xmin,
                    double fmin)

Description copied from class: BracketSearchMinimizer.Solution

Initializes the algorithm states with initial \(x_{min}\) and \(f_{min}\) before iterations. The function value of the initial minimum point is evaluated in this class. If the subclass algorithm needs the computed function value, it can override this method to avoid an unnecessary evaluation. By default, the implementation is empty. If the subclass algorithm does not need to initialize states from the function value, no overriding is needed.

Overrides:

init in class BracketSearchMinimizer.Solution

Parameters:

xmin - the initial minimum point

fmin - the function value of the initial minimum point

isMinFound

protected boolean isMinFound()

the convergence criterion The search stops when

\((x_u - x_l) < 2 \left | x \right | \varepsilon \) \(\left | \rm xmin - \rm mid \right | < \left | x \right | \varepsilon\)

\((x_u - x_l) / 2 + \left | \rm xmin - \rm mid \right | < 2 \left | x \right | \varepsilon \approx \rm tol_2\)

Specified by:

isMinFound in class BracketSearchMinimizer.Solution

Returns:

true if the minimum is found

See Also:

"Chapter 10.3, Numerical Recipes."

xnext

protected double xnext()

Description copied from class: BracketSearchMinimizer.Solution

Compute the next best estimate within the bracketing interval. A particular univariate minimization algorithm implements the logic in this method.

Specified by:

xnext in class BracketSearchMinimizer.Solution

Returns:

the next best guess of the minimizer

updateStates

protected void updateStates()

Description copied from class: BracketSearchMinimizer.Solution

Update the bracketing interval and the best min found so far.

Overrides:

updateStates in class BracketSearchMinimizer.Solution