Base class for all bracketing Secant-based methods for root-finding (approximating a zero of a univariate real function).

Implementation of the Regula Falsi and Illinois methods is based on the following article: M. Dowell and P. Jarratt, A modified regula falsi method for computing the root of an equation, BIT Numerical Mathematics, volume 11, number 2, pages 168-174, Springer, 1971.

Implementation of the Pegasus method is based on the following article: M. Dowell and P. Jarratt, The "Pegasus" method for computing the root of an equation, BIT Numerical Mathematics, volume 12, number 4, pages 503-508, Springer, 1972.

The Secant method is not a bracketing method, so it is not implemented here. It has a separate implementation.

Nested and Inner Type Summary

Modifier and Type	Class and Description
protected static enum	BaseSecantSolver.Method Secant-based root-finding methods.

Field Summary

Modifier and Type	Field and Description
private AllowedSolution	allowed The kinds of solutions that the algorithm may accept.
protected static final double	DEFAULT_ABSOLUTE_ACCURACY Default absolute accuracy.
private final BaseSecantSolver.Method	method The Secant-based root-finding method to use.

Constructor Summary

Access	Constructor and Description
protected	BaseSecantSolver(final double Absolute accuracy. absoluteAccuracy, final BaseSecantSolver.Method Secant-based root-finding method to use. method) Construct a solver.
protected	BaseSecantSolver(final double Relative accuracy. relativeAccuracy, final double Absolute accuracy. absoluteAccuracy, final BaseSecantSolver.Method Secant-based root-finding method to use. method) Construct a solver.
protected	BaseSecantSolver(final double Maximum relative error. relativeAccuracy, final double Maximum absolute error. absoluteAccuracy, final double Maximum function value error. functionValueAccuracy, final BaseSecantSolver.Method Secant-based root-finding method to use method) Construct a solver.

Method Summary

Modifier and Type	Method and Description
protected final double	doSolve() Implements abstract org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.doSolve. Method for implementing actual optimization algorithms in derived classes.
public double	solve(final int Maximum number of evaluations. maxEval, final UnivariateFunction Function to solve. f, final double Lower bound for the interval. min, final double Upper bound for the interval. max, final AllowedSolution The kind of solutions that the root-finding algorithm may accept as solutions. allowedSolution) Implements org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve. Solve for a zero in the given interval.
public double	solve(final int Maximum number of evaluations. maxEval, final UnivariateFunction Function to solve. f, final double Lower bound for the interval. min, final double Upper bound for the interval. max, final double Start value to use. startValue, final AllowedSolution The kind of solutions that the root-finding algorithm may accept as solutions. allowedSolution) Implements org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve. Solve for a zero in the given interval, start at `startValue`.
public double	solve(final int Maximum number of evaluations. maxEval, final UnivariateFunction Function to solve. f, final double Lower bound for the interval. min, final double Upper bound for the interval. max, final double Start value to use. startValue) Overrides org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve. Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Solve for a zero in the given interval, start at `startValue`.

Field Detail

allowed	back to summary
private AllowedSolution allowed The kinds of solutions that the algorithm may accept.

DEFAULT_ABSOLUTE_ACCURACY	back to summary
protected static final double DEFAULT_ABSOLUTE_ACCURACY Default absolute accuracy.

method	back to summary
private final BaseSecantSolver.Method method The Secant-based root-finding method to use.

Constructor Detail

BaseSecantSolver	back to summary
protected BaseSecantSolver(final double absoluteAccuracy, final BaseSecantSolver.Method method) Construct a solver. Parameters absoluteAccuracy:double Absolute accuracy. method:BaseSecantSolver.Method Secant-based root-finding method to use.

BaseSecantSolver

back to summary

protected BaseSecantSolver(final double absoluteAccuracy, final BaseSecantSolver.Method method)

Construct a solver.

Parameters

absoluteAccuracy:double: Absolute accuracy.
method:BaseSecantSolver.Method: Secant-based root-finding method to use.

BaseSecantSolver	back to summary
protected BaseSecantSolver(final double relativeAccuracy, final double absoluteAccuracy, final BaseSecantSolver.Method method) Construct a solver. Parameters relativeAccuracy:double Relative accuracy. absoluteAccuracy:double Absolute accuracy. method:BaseSecantSolver.Method Secant-based root-finding method to use.

BaseSecantSolver

back to summary

protected BaseSecantSolver(final double relativeAccuracy, final double absoluteAccuracy, final BaseSecantSolver.Method method)

Construct a solver.

Parameters

relativeAccuracy:double: Relative accuracy.
absoluteAccuracy:double: Absolute accuracy.
method:BaseSecantSolver.Method: Secant-based root-finding method to use.

BaseSecantSolver	back to summary
protected BaseSecantSolver(final double relativeAccuracy, final double absoluteAccuracy, final double functionValueAccuracy, final BaseSecantSolver.Method method) Construct a solver. Parameters relativeAccuracy:double Maximum relative error. absoluteAccuracy:double Maximum absolute error. functionValueAccuracy:double Maximum function value error. method:BaseSecantSolver.Method Secant-based root-finding method to use

BaseSecantSolver

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protected BaseSecantSolver(final double relativeAccuracy, final double absoluteAccuracy, final double functionValueAccuracy, final BaseSecantSolver.Method method)

Construct a solver.

Parameters

relativeAccuracy:double: Maximum relative error.
absoluteAccuracy:double: Maximum absolute error.
functionValueAccuracy:double: Maximum function value error.
method:BaseSecantSolver.Method: Secant-based root-finding method to use

Method Detail

doSolve	back to summary
protected final double doSolve() throws ConvergenceException Implements abstract org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.doSolve. Doc from org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.doSolve. Method for implementing actual optimization algorithms in derived classes. Returns:double the root. Annotations @Override Exceptions ConvergenceException: if the algorithm failed due to finite precision.

doSolve

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protected final double doSolve() throws ConvergenceException

Implements abstract org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.doSolve.

Doc from org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.doSolve.

Method for implementing actual optimization algorithms in derived classes.

Returns:double

the root.

Annotations

@Override

Exceptions

ConvergenceException:: if the algorithm failed due to finite precision.

solve	back to summary
public double solve(final int maxEval, final UnivariateFunction f, final double min, final double max, final AllowedSolution allowedSolution) Implements org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve. Doc from org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve. Solve for a zero in the given interval. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root. Parameters maxEval:int Maximum number of evaluations. f:UnivariateFunction Function to solve. min:double Lower bound for the interval. max:double Upper bound for the interval. allowedSolution:AllowedSolution The kind of solutions that the root-finding algorithm may accept as solutions. Returns:double A value where the function is zero.

solve

back to summary

public double solve(final int maxEval, final UnivariateFunction f, final double min, final double max, final AllowedSolution allowedSolution)

Implements org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve.

Doc from org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve.

Solve for a zero in the given interval. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root.

Parameters

maxEval:int: Maximum number of evaluations.
f:UnivariateFunction: Function to solve.
min:double: Lower bound for the interval.
max:double: Upper bound for the interval.
allowedSolution:AllowedSolution: The kind of solutions that the root-finding algorithm may accept as solutions.

Returns:double

A value where the function is zero.

solve back to summary

solve	back to summary
public double solve(final int maxEval, final UnivariateFunction f, final double min, final double max, final double startValue, final AllowedSolution allowedSolution) Implements org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve. Doc from org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve. Solve for a zero in the given interval, start at `startValue`. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root. Parameters maxEval:int Maximum number of evaluations. f:UnivariateFunction Function to solve. min:double Lower bound for the interval. max:double Upper bound for the interval. startValue:double Start value to use. allowedSolution:AllowedSolution The kind of solutions that the root-finding algorithm may accept as solutions. Returns:double A value where the function is zero.

public double solve(final int maxEval, final UnivariateFunction f, final double min, final double max, final double startValue, final AllowedSolution allowedSolution)

Implements org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve.

Doc from org.apache.commons.math3.analysis.solvers.BracketedUnivariateSolver.solve.

Solve for a zero in the given interval, start at startValue. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root.

Parameters

maxEval:int: Maximum number of evaluations.
f:UnivariateFunction: Function to solve.
min:double: Lower bound for the interval.
max:double: Upper bound for the interval.
startValue:double: Start value to use.
allowedSolution:AllowedSolution: The kind of solutions that the root-finding algorithm may accept as solutions.

Returns:double

A value where the function is zero.

solve back to summary

solve	back to summary
public double solve(final int maxEval, final UnivariateFunction f, final double min, final double max, final double startValue) Overrides org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve. Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve. Solve for a zero in the given interval, start at `startValue`. A solver may require that the interval brackets a single zero root. Solvers that do require bracketing should be able to handle the case where one of the endpoints is itself a root. Parameters maxEval:int Maximum number of evaluations. f:UnivariateFunction Function to solve. min:double Lower bound for the interval. max:double Upper bound for the interval. startValue:double Start value to use. Returns:double a value where the function is zero. Annotations @Override

public double solve(final int maxEval, final UnivariateFunction f, final double min, final double max, final double startValue)

Overrides org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver.solve.

Implements org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve.

Doc from org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver.solve.

Parameters

maxEval:int: Maximum number of evaluations.
f:UnivariateFunction: Function to solve.
min:double: Lower bound for the interval.
max:double: Upper bound for the interval.
startValue:double: Start value to use.

Returns:double

a value where the function is zero.

Annotations

@Override

org.apache.commons.math3.analysis.solvers back to summary

protected final Enum BaseSecantSolver.Method

Class Inheritance

extends Enum<BaseSecantSolver.Method>

java.lang.Object
java.lang.Enum
org.apache.commons.math3.analysis.solvers.BaseSecantSolver.Method

Secant-based root-finding methods.

Field Summary

Modifier and Type	Field and Description
public static final BaseSecantSolver.Method	ILLINOIS The `Illinois` method.
public static final BaseSecantSolver.Method	PEGASUS The `Pegasus` method.
public static final BaseSecantSolver.Method	REGULA_FALSI The `Regula Falsi` or False Position method.

Constructor Summary

Access	Constructor and Description
private	Method()

Method Summary

Modifier and Type	Method and Description
public static BaseSecantSolver.Method	valueOf(String name)
public static BaseSecantSolver.Method[]	values()

Inherited from java.lang.Enum:: clone compareTo describeConstable equals finalize getDeclaringClass hashCode name ordinal toString valueOf

Field Detail

ILLINOIS	back to summary
public static final BaseSecantSolver.Method ILLINOIS The `Illinois` method.

PEGASUS	back to summary
public static final BaseSecantSolver.Method PEGASUS The `Pegasus` method.

REGULA_FALSI	back to summary
public static final BaseSecantSolver.Method REGULA_FALSI The `Regula Falsi` or False Position method.

Constructor Detail

Method	back to summary
private Method()

Method Detail

valueOf	back to summary
public static BaseSecantSolver.Method valueOf(String name)

values	back to summary
public static BaseSecantSolver.Method[] values()

public abstract Class BaseSecantSolver

Nested and Inner Type Summary

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail

protected final Enum BaseSecantSolver.Method

Field Summary

Constructor Summary

Method Summary

Field Detail

Constructor Detail

Method Detail