org.hipparchus.analysis.solvers

Class BaseSecantSolver

java.lang.Object

org.hipparchus.analysis.solvers.BaseAbstractUnivariateSolver<UnivariateFunction>

org.hipparchus.analysis.solvers.AbstractUnivariateSolver

org.hipparchus.analysis.solvers.BaseSecantSolver

All Implemented Interfaces:

BaseUnivariateSolver<UnivariateFunction>, BracketedUnivariateSolver<UnivariateFunction>, UnivariateSolver

Direct Known Subclasses:

IllinoisSolver, PegasusSolver, RegulaFalsiSolver

public abstract class BaseSecantSolver
extends AbstractUnivariateSolver
implements BracketedUnivariateSolver<UnivariateFunction>

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 Class Summary

Nested Classes

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

Nested classes/interfaces inherited from interface org.hipparchus.analysis.solvers.BracketedUnivariateSolver

BracketedUnivariateSolver.Interval

Field Summary

Fields

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

Constructor Summary

Constructors

Modifier	Constructor and Description
protected	BaseSecantSolver(double absoluteAccuracy, BaseSecantSolver.Method method) Construct a solver.
protected	BaseSecantSolver(double relativeAccuracy, double absoluteAccuracy, BaseSecantSolver.Method method) Construct a solver.
protected	BaseSecantSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy, BaseSecantSolver.Method method) Construct a solver.

Method Summary

Modifier and Type	Method and Description
protected double	doSolve() Method for implementing actual optimization algorithms in derived classes.
protected BracketedUnivariateSolver.Interval	doSolveInterval() Find a root and return the containing interval.
double	solve(int maxEval, UnivariateFunction f, double min, double max, AllowedSolution allowedSolution) Solve for a zero in the given interval.
double	solve(int maxEval, UnivariateFunction f, double min, double max, double startValue) Solve for a zero in the given interval, start at startValue.
double	solve(int maxEval, UnivariateFunction f, double min, double max, double startValue, AllowedSolution allowedSolution) Solve for a zero in the given interval, start at startValue.
BracketedUnivariateSolver.Interval	solveInterval(int maxEval, UnivariateFunction f, double min, double max, double startValue) Solve for a zero in the given interval and return a tolerance interval surrounding the root.

Methods inherited from class org.hipparchus.analysis.solvers.BaseAbstractUnivariateSolver

computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, getMaxEvaluations, getMin, getRelativeAccuracy, getStartValue, incrementEvaluationCount, isBracketing, isSequence, setup, 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.hipparchus.analysis.solvers.BracketedUnivariateSolver

solveInterval

Methods inherited from interface org.hipparchus.analysis.solvers.BaseUnivariateSolver

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

Field Detail

DEFAULT_ABSOLUTE_ACCURACY

protected static final double DEFAULT_ABSOLUTE_ACCURACY

Default absolute accuracy.

See Also:

Constant Field Values

Constructor Detail

BaseSecantSolver

protected BaseSecantSolver(double absoluteAccuracy,
                           BaseSecantSolver.Method method)

Construct a solver.

Parameters:

absoluteAccuracy - Absolute accuracy.

method - Secant-based root-finding method to use.

BaseSecantSolver

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

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

method - Secant-based root-finding method to use.

BaseSecantSolver

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

Construct a solver.

Parameters:

relativeAccuracy - Maximum relative error.

absoluteAccuracy - Maximum absolute error.

functionValueAccuracy - Maximum function value error.

method - Secant-based root-finding method to use

Method Detail

solve

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

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.

Specified by:

solve in interface BracketedUnivariateSolver<UnivariateFunction>

Parameters:

maxEval - Maximum number of evaluations.

f - Function to solve.

min - Lower bound for the interval.

max - Upper bound for the interval.

allowedSolution - The kind of solutions that the root-finding algorithm may accept as solutions.

Returns:

A value where the function is zero.

solve

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

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.

Specified by:

solve in interface BracketedUnivariateSolver<UnivariateFunction>

Parameters:

maxEval - Maximum number of evaluations.

f - Function to solve.

min - Lower bound for the interval.

max - Upper bound for the interval.

startValue - Start value to use.

allowedSolution - The kind of solutions that the root-finding algorithm may accept as solutions.

Returns:

A value where the function is zero.

solve

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

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.

Specified by:

solve in interface BaseUnivariateSolver<UnivariateFunction>

Overrides:

solve in class BaseAbstractUnivariateSolver<UnivariateFunction>

Parameters:

maxEval - Maximum number of evaluations.

f - Function to solve.

min - Lower bound for the interval.

max - Upper bound for the interval.

startValue - Start value to use.

Returns:

a value where the function is zero.

solveInterval

public BracketedUnivariateSolver.Interval solveInterval(int maxEval,
                                                        UnivariateFunction f,
                                                        double min,
                                                        double max,
                                                        double startValue)
                                                 throws MathIllegalArgumentException,
                                                        MathIllegalStateException

Solve for a zero in the given interval and return a tolerance interval surrounding the root.

It is required that the starting interval brackets a root or that the function value at either end point is 0.0.

Specified by:

solveInterval in interface BracketedUnivariateSolver<UnivariateFunction>

Parameters:

maxEval - Maximum number of evaluations.

f - Function to solve.

min - Lower bound for the interval.

max - Upper bound for the interval. Must be greater than min.

startValue - start value to use. Must be in the interval [min, max].

Returns:

an interval [ta, tb] such that for some t in [ta, tb] f(t) == 0.0 or has a step wise discontinuity that crosses zero. Both end points also satisfy the convergence criteria so either one could be used as the root. That is the interval satisfies the condition (| tb - ta | <= absolute accuracy + max(ta, tb) * relative accuracy) or ( max(|f(ta)|, |f(tb)|) <= BaseUnivariateSolver.getFunctionValueAccuracy()) or there are no floating point numbers between ta and tb. The width of the interval (tb - ta) may be zero.

Throws:

MathIllegalArgumentException - if the arguments do not satisfy the requirements specified by the solver.

MathIllegalStateException - if the allowed number of evaluations is exceeded.

doSolve

protected final double doSolve()
                        throws MathIllegalStateException

Method for implementing actual optimization algorithms in derived classes.

Specified by:

doSolve in class BaseAbstractUnivariateSolver<UnivariateFunction>

Returns:

the root.

Throws:

MathIllegalStateException - if the algorithm failed due to finite precision.

doSolveInterval

protected final BracketedUnivariateSolver.Interval doSolveInterval()
                                                            throws MathIllegalStateException

Find a root and return the containing interval.

Returns:

an interval containing the root such that the selected end point meets the convergence criteria.

Throws:

MathIllegalStateException - if convergence fails.