Apache Commons Math 3.6.1 · org.apache.commons.math3.optim.univariate.BrentOptimizer

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.

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

Constructor Summary

Access	Constructor and Description
public	BrentOptimizer(double Relative threshold. rel, double Absolute threshold. abs, ConvergenceChecker<UnivariatePointValuePair> Additional, user-defined, convergence checking procedure. checker) The arguments are used implement the original stopping criterion of Brent's algorithm.
public	BrentOptimizer(double Relative threshold. rel, double Absolute threshold. abs) The arguments are used for implementing the original stopping criterion of Brent's algorithm.

Method Summary

Modifier and Type	Method and Description
private UnivariatePointValuePair	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. best(UnivariatePointValuePair Point and value. a, UnivariatePointValuePair Point and value. b, boolean `true` if the selected point must be the one with the lowest value. isMinim) Selects the best of two points.
protected UnivariatePointValuePair	doOptimize() Implements abstract org.apache.commons.math3.optim.BaseOptimizer.doOptimize. Performs the bulk of the optimization algorithm.

Inherited from org.apache.commons.math3.optim.univariate.UnivariateOptimizer:: computeObjectiveValue getGoalType getMax getMin getStartValue optimize parseOptimizationData

Field Detail

absoluteThreshold	back to summary
private final double absoluteThreshold Absolute threshold.

GOLDEN_SECTION	back to summary
private static final double GOLDEN_SECTION Golden section.

MIN_RELATIVE_TOLERANCE	back to summary
private static final double MIN_RELATIVE_TOLERANCE Minimum relative tolerance.

relativeThreshold	back to summary
private final double relativeThreshold Relative threshold.

Constructor Detail

BrentOptimizer back to summary

BrentOptimizer	back to summary
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:double Relative threshold. abs:double Absolute threshold. checker:ConvergenceChecker<UnivariatePointValuePair> Additional, user-defined, convergence checking procedure. Exceptions NotStrictlyPositiveException: if `abs <= 0`. NumberIsTooSmallException: if `rel < 2 * Math.ulp(1d)`.

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:double: Relative threshold.
abs:double: Absolute threshold.
checker:ConvergenceChecker<UnivariatePointValuePair>: Additional, user-defined, convergence checking procedure.

Exceptions

NotStrictlyPositiveException:: if abs <= 0.
NumberIsTooSmallException:: if rel < 2 * Math.ulp(1d).

BrentOptimizer back to summary

BrentOptimizer	back to summary
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:double Relative threshold. abs:double Absolute threshold. Exceptions NotStrictlyPositiveException: if `abs <= 0`. NumberIsTooSmallException: if `rel < 2 * Math.ulp(1d)`.

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:double: Relative threshold.
abs:double: Absolute threshold.

Exceptions

NotStrictlyPositiveException:: if abs <= 0.
NumberIsTooSmallException:: if rel < 2 * Math.ulp(1d).

Method Detail

best back to summary

best	back to summary
private UnivariatePointValuePair best(UnivariatePointValuePair a, UnivariatePointValuePair b, boolean isMinim) Selects the best of two points. Parameters a:UnivariatePointValuePair Point and value. b:UnivariatePointValuePair Point and value. isMinim:boolean `true` if the selected point must be the one with the lowest value. Returns:UnivariatePointValuePair the best point, or `null` if `a` and `b` are both `null`. When `a` and `b` have the same function value, `a` is returned.

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

Selects the best of two points.

Parameters

a:UnivariatePointValuePair: Point and value.
b:UnivariatePointValuePair: Point and value.
isMinim:boolean: true if the selected point must be the one with the lowest value.

Returns:UnivariatePointValuePair

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

doOptimize	back to summary
protected UnivariatePointValuePair doOptimize() Implements abstract org.apache.commons.math3.optim.BaseOptimizer.doOptimize. Doc from org.apache.commons.math3.optim.BaseOptimizer.doOptimize. Performs the bulk of the optimization algorithm. Returns:UnivariatePointValuePair the point/value pair giving the optimal value of the objective function. Annotations @Override

doOptimize

back to summary

protected UnivariatePointValuePair doOptimize()

Implements abstract org.apache.commons.math3.optim.BaseOptimizer.doOptimize.

Doc from org.apache.commons.math3.optim.BaseOptimizer.doOptimize.

Performs the bulk of the optimization algorithm.

Returns:UnivariatePointValuePair

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

Annotations

@Override

public Class BrentOptimizer

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