Package org.apache.commons.math3.optim.univariate

Class BrentOptimizer

java.lang.Object

org.apache.commons.math3.optim.BaseOptimizer<UnivariatePointValuePair>

org.apache.commons.math3.optim.univariate.UnivariateOptimizer

org.apache.commons.math3.optim.univariate.BrentOptimizer

public class BrentOptimizer
extends UnivariateOptimizer

For a function defined on some interval (lo, hi), this class finds an approximation x to the point at which the function attains its minimum. It implements Richard Brent's algorithm (from his book "Algorithms for Minimization without Derivatives", p. 79) for finding minima of real univariate functions.
This code is an adaptation, partly based on the Python code from SciPy (module "optimize.py" v0.5); the original algorithm is also modified

• to use an initial guess provided by the user,
• to ensure that the best point encountered is the one returned.

Since:

2.0

Field Summary

Fields

Modifier and Type	Field	Description
private double	absoluteThreshold	Absolute threshold.
private static double	GOLDEN_SECTION	Golden section.
private static double	MIN_RELATIVE_TOLERANCE	Minimum relative tolerance.
private double	relativeThreshold	Relative threshold.

Fields inherited from class org.apache.commons.math3.optim.BaseOptimizer

evaluations, iterations

Constructor Summary

Constructors

Constructor	Description
BrentOptimizer(double rel, double abs)	The arguments are used for implementing the original stopping criterion of Brent's algorithm.
BrentOptimizer(double rel, double abs, ConvergenceChecker<UnivariatePointValuePair> checker)	The arguments are used implement the original stopping criterion of Brent's algorithm.

Method Summary

Modifier and Type	Method	Description
private UnivariatePointValuePair	best(UnivariatePointValuePair a, UnivariatePointValuePair b, boolean isMinim)	Selects the best of two points.
protected UnivariatePointValuePair	doOptimize()	Performs the bulk of the optimization algorithm.

Methods inherited from class org.apache.commons.math3.optim.univariate.UnivariateOptimizer

computeObjectiveValue, getGoalType, getMax, getMin, getStartValue, optimize, parseOptimizationData

Methods inherited from class org.apache.commons.math3.optim.BaseOptimizer

getConvergenceChecker, getEvaluations, getIterations, getMaxEvaluations, getMaxIterations, incrementEvaluationCount, incrementIterationCount, optimize

Methods inherited from class java.lang.Object

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

Field Detail

GOLDEN_SECTION

private static final double GOLDEN_SECTION

Golden section.

MIN_RELATIVE_TOLERANCE

private static final double MIN_RELATIVE_TOLERANCE

Minimum relative tolerance.

relativeThreshold

private final double relativeThreshold

Relative threshold.

absoluteThreshold

private final double absoluteThreshold

Absolute threshold.

Constructor Detail

BrentOptimizer

public BrentOptimizer(double rel,
                      double abs,
                      ConvergenceChecker<UnivariatePointValuePair> checker)

The arguments are used implement the original stopping criterion of Brent's algorithm. abs and rel define a tolerance tol = rel |x| + abs. rel should be no smaller than 2 macheps and preferably not much less than sqrt(macheps), where macheps is the relative machine precision. abs must be positive.

Parameters:

rel - Relative threshold.

abs - Absolute threshold.

checker - Additional, user-defined, convergence checking procedure.

Throws:

NotStrictlyPositiveException - if abs <= 0.

NumberIsTooSmallException - if rel < 2 * Math.ulp(1d).

BrentOptimizer

public BrentOptimizer(double rel,
                      double abs)

The arguments are used for implementing the original stopping criterion of Brent's algorithm. abs and rel define a tolerance tol = rel |x| + abs. rel should be no smaller than 2 macheps and preferably not much less than sqrt(macheps), where macheps is the relative machine precision. abs must be positive.

Parameters:

rel - Relative threshold.

abs - Absolute threshold.

Throws:

NotStrictlyPositiveException - if abs <= 0.

NumberIsTooSmallException - if rel < 2 * Math.ulp(1d).

Method Detail

doOptimize

protected UnivariatePointValuePair doOptimize()

Performs the bulk of the optimization algorithm.

Specified by:

doOptimize in class BaseOptimizer<UnivariatePointValuePair>

Returns:

the point/value pair giving the optimal value of the objective function.

best

private UnivariatePointValuePair best(UnivariatePointValuePair a,
                                      UnivariatePointValuePair b,
                                      boolean isMinim)

Selects the best of two points.

Parameters:

a - Point and value.

b - Point and value.

isMinim - true if the selected point must be the one with the lowest value.

Returns:

the best point, or null if a and b are both null. When a and b have the same function value, a is returned.