Package org.apache.commons.math3.analysis.solvers

Class BrentSolver

java.lang.Object

org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<UnivariateFunction>

org.apache.commons.math3.analysis.solvers.AbstractUnivariateSolver

org.apache.commons.math3.analysis.solvers.BrentSolver

All Implemented Interfaces:

BaseUnivariateSolver<UnivariateFunction>, UnivariateSolver

public class BrentSolver
extends AbstractUnivariateSolver

This class implements the Brent algorithm for finding zeros of real univariate functions. The function should be continuous but not necessarily smooth. The solve method returns a zero x of the function f in the given interval [a, b] to within a tolerance 2 eps abs(x) + t where eps is the relative accuracy and t is the absolute accuracy.

The given interval must bracket the root.

The reference implementation is given in chapter 4 of

Algorithms for Minimization Without Derivatives, Richard P. Brent, Dover, 2002

See Also:

BaseAbstractUnivariateSolver

Field Summary

Fields

Modifier and Type	Field	Description
private static double	DEFAULT_ABSOLUTE_ACCURACY	Default absolute accuracy.

Constructor Summary

Constructors

Constructor	Description
BrentSolver()	Construct a solver with default absolute accuracy (1e-6).
BrentSolver(double absoluteAccuracy)	Construct a solver.
BrentSolver(double relativeAccuracy, double absoluteAccuracy)	Construct a solver.
BrentSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy)	Construct a solver.

Method Summary

Modifier and Type	Method	Description
private double	brent(double lo, double hi, double fLo, double fHi)	Search for a zero inside the provided interval.
protected double	doSolve()	Method for implementing actual optimization algorithms in derived classes.

Methods inherited from class org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver

computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, getMaxEvaluations, getMin, getRelativeAccuracy, getStartValue, incrementEvaluationCount, isBracketing, isSequence, setup, solve, solve, solve, verifyBracketing, verifyInterval, verifySequence

Methods inherited from class java.lang.Object

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

Methods inherited from interface org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver

getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMaxEvaluations, getRelativeAccuracy, solve, solve, solve

Field Detail

DEFAULT_ABSOLUTE_ACCURACY

private static final double DEFAULT_ABSOLUTE_ACCURACY

Default absolute accuracy.

See Also:

Constant Field Values

Constructor Detail

BrentSolver

public BrentSolver()

Construct a solver with default absolute accuracy (1e-6).

BrentSolver

public BrentSolver(double absoluteAccuracy)

Construct a solver.

Parameters:

absoluteAccuracy - Absolute accuracy.

BrentSolver

public BrentSolver(double relativeAccuracy,
                   double absoluteAccuracy)

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

BrentSolver

public BrentSolver(double relativeAccuracy,
                   double absoluteAccuracy,
                   double functionValueAccuracy)

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

functionValueAccuracy - Function value accuracy.

See Also:

BaseAbstractUnivariateSolver(double,double,double)

Method Detail

doSolve

protected double doSolve()
                  throws NoBracketingException,
                         TooManyEvaluationsException,
                         NumberIsTooLargeException

Method for implementing actual optimization algorithms in derived classes.

Specified by:

doSolve in class BaseAbstractUnivariateSolver<UnivariateFunction>

Returns:

the root.

Throws:

NoBracketingException - if the initial search interval does not bracket a root and the solver requires it.

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

NumberIsTooLargeException

brent

private double brent(double lo,
                     double hi,
                     double fLo,
                     double fHi)

Search for a zero inside the provided interval. This implementation is based on the algorithm described at page 58 of the book

Algorithms for Minimization Without Derivatives, Richard P. Brent, Dover 0-486-41998-3

Parameters:

lo - Lower bound of the search interval.

hi - Higher bound of the search interval.

fLo - Function value at the lower bound of the search interval.

fHi - Function value at the higher bound of the search interval.

Returns:

the value where the function is zero.