org.hipparchus.analysis.solvers

Class BracketingNthOrderBrentSolver

java.lang.Object

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

org.hipparchus.analysis.solvers.AbstractUnivariateSolver

org.hipparchus.analysis.solvers.BracketingNthOrderBrentSolver

All Implemented Interfaces:

BaseUnivariateSolver<UnivariateFunction>, BracketedUnivariateSolver<UnivariateFunction>, UnivariateSolver

public class BracketingNthOrderBrentSolver
extends AbstractUnivariateSolver
implements BracketedUnivariateSolver<UnivariateFunction>

This class implements a modification of the Brent algorithm.

The changes with respect to the original Brent algorithm are:

• the returned value is chosen in the current interval according to user specified AllowedSolution,
• the maximal order for the invert polynomial root search is user-specified instead of being invert quadratic only

The given interval must bracket the root.

Nested Class Summary

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

BracketedUnivariateSolver.Interval

Constructor Summary

Constructors

Constructor and Description
BracketingNthOrderBrentSolver() Construct a solver with default accuracy and maximal order (1e-6 and 5 respectively)
BracketingNthOrderBrentSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy, int maximalOrder) Construct a solver.
BracketingNthOrderBrentSolver(double relativeAccuracy, double absoluteAccuracy, int maximalOrder) Construct a solver.
BracketingNthOrderBrentSolver(double absoluteAccuracy, int maximalOrder) 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.
int	getMaximalOrder() Get the maximal order.
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, 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, 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, solve

Constructor Detail

BracketingNthOrderBrentSolver

public BracketingNthOrderBrentSolver()

Construct a solver with default accuracy and maximal order (1e-6 and 5 respectively)

BracketingNthOrderBrentSolver

public BracketingNthOrderBrentSolver(double absoluteAccuracy,
                                     int maximalOrder)
                              throws MathIllegalArgumentException

Construct a solver.

Parameters:

absoluteAccuracy - Absolute accuracy.

maximalOrder - maximal order.

Throws:

MathIllegalArgumentException - if maximal order is lower than 2

BracketingNthOrderBrentSolver

public BracketingNthOrderBrentSolver(double relativeAccuracy,
                                     double absoluteAccuracy,
                                     int maximalOrder)
                              throws MathIllegalArgumentException

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

maximalOrder - maximal order.

Throws:

MathIllegalArgumentException - if maximal order is lower than 2

BracketingNthOrderBrentSolver

public BracketingNthOrderBrentSolver(double relativeAccuracy,
                                     double absoluteAccuracy,
                                     double functionValueAccuracy,
                                     int maximalOrder)
                              throws MathIllegalArgumentException

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

functionValueAccuracy - Function value accuracy.

maximalOrder - maximal order.

Throws:

MathIllegalArgumentException - if maximal order is lower than 2

Method Detail

getMaximalOrder

public int getMaximalOrder()

Get the maximal order.

Returns:

maximal order

doSolve

protected double doSolve()

Method for implementing actual optimization algorithms in derived classes.

Specified by:

doSolve in class BaseAbstractUnivariateSolver<UnivariateFunction>

Returns:

the root.

doSolveInterval

protected BracketedUnivariateSolver.Interval doSolveInterval()

Find a root and return the containing interval.

Returns:

an interval containing the root such that both end points meet the convergence criteria.

solve

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

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.

Throws:

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

MathIllegalStateException - if the allowed number of evaluations is exceeded.

solve

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

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.

Throws:

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

MathIllegalStateException - if the allowed number of evaluations is exceeded.

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.