org.apache.commons.math3.optimization.univariate
Class BrentOptimizer

java.lang.Object
  extended by org.apache.commons.math3.optimization.univariate.BaseAbstractUnivariateOptimizer
      extended by org.apache.commons.math3.optimization.univariate.BrentOptimizer
All Implemented Interfaces:
BaseOptimizer<UnivariatePointValuePair>, BaseUnivariateOptimizer<UnivariateFunction>, UnivariateOptimizer
Direct Known Subclasses:
PowellOptimizer.LineSearch

public class BrentOptimizer
extends BaseAbstractUnivariateOptimizer

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

Since:
2.0
Version:
$Id: BrentOptimizer.java 1244107 2012-02-14 16:17:55Z erans $

Field Summary
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.
 
Constructor Summary
BrentOptimizer(double rel, double abs)
          The arguments are used implement 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
protected  UnivariatePointValuePair doOptimize()
          Method for implementing actual optimization algorithms in derived classes.
 
Methods inherited from class org.apache.commons.math3.optimization.univariate.BaseAbstractUnivariateOptimizer
computeObjectiveValue, getConvergenceChecker, getEvaluations, getGoalType, getMax, getMaxEvaluations, getMin, getStartValue, optimize, 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 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.
Throws:
NotStrictlyPositiveException - if abs <= 0.
NumberIsTooSmallException - if rel < 2 * Math.ulp(1d).
Method Detail

doOptimize

protected UnivariatePointValuePair doOptimize()
Method for implementing actual optimization algorithms in derived classes.

Specified by:
doOptimize in class BaseAbstractUnivariateOptimizer
Returns:
the optimum and its corresponding function value.


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