Package org.apache.commons.math4.legacy.analysis.solvers

Class BaseAbstractUnivariateSolver<FUNC extends UnivariateFunction>

java.lang.Object

org.apache.commons.math4.legacy.analysis.solvers.BaseAbstractUnivariateSolver<FUNC>

Type Parameters:

FUNC - Type of function to solve.

All Implemented Interfaces:

BaseUnivariateSolver<FUNC>

Direct Known Subclasses:

AbstractPolynomialSolver, AbstractUnivariateDifferentiableSolver, AbstractUnivariateSolver

public abstract class BaseAbstractUnivariateSolver<FUNC extends UnivariateFunction>
extends Object
implements BaseUnivariateSolver<FUNC>

Provide a default implementation for several functions useful to generic solvers. The default values for relative and function tolerances are 1e-14 and 1e-15, respectively. It is however highly recommended to not rely on the default, but rather carefully consider values that match user's expectations, as well as the specifics of each implementation.

Since:

2.0

Constructor Summary

Constructors

Modifier	Constructor	Description
protected	BaseAbstractUnivariateSolver(double absoluteAccuracy)	Construct a solver with given absolute accuracy.
protected	BaseAbstractUnivariateSolver(double relativeAccuracy, double absoluteAccuracy)	Construct a solver with given accuracies.
protected	BaseAbstractUnivariateSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy)	Construct a solver with given accuracies.

Method Summary

Modifier and Type	Method	Description
protected double	computeObjectiveValue(double point)	Compute the objective function value.
protected abstract double	doSolve()	Method for implementing actual optimization algorithms in derived classes.
double	getAbsoluteAccuracy()	Get the absolute accuracy of the solver.
int	getEvaluations()	Get the number of evaluations of the objective function.
double	getFunctionValueAccuracy()	Get the function value accuracy of the solver.
double	getMax()
int	getMaxEvaluations()	Get the maximum number of function evaluations.
double	getMin()
double	getRelativeAccuracy()	Get the relative accuracy of the solver.
double	getStartValue()
protected void	incrementEvaluationCount()	Increment the evaluation count by one.
protected boolean	isBracketing(double lower, double upper)	Check whether the function takes opposite signs at the endpoints.
protected boolean	isSequence(double start, double mid, double end)	Check whether the arguments form a (strictly) increasing sequence.
protected void	setup(int maxEval, FUNC f, double min, double max, double startValue)	Prepare for computation.
double	solve(int maxEval, FUNC f, double startValue)	Solve for a zero in the vicinity of startValue.
double	solve(int maxEval, FUNC f, double min, double max)	Solve for a zero root in the given interval.
double	solve(int maxEval, FUNC f, double min, double max, double startValue)	Solve for a zero in the given interval, start at startValue.
protected void	verifyBracketing(double lower, double upper)	Check that the endpoints specify an interval and the function takes opposite signs at the endpoints.
protected void	verifyInterval(double lower, double upper)	Check that the endpoints specify an interval.
protected void	verifySequence(double lower, double initial, double upper)	Check that lower < initial < upper.

Methods inherited from class java.lang.Object

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

Constructor Detail

BaseAbstractUnivariateSolver

protected BaseAbstractUnivariateSolver(double absoluteAccuracy)

Construct a solver with given absolute accuracy.

Parameters:

absoluteAccuracy - Maximum absolute error.

BaseAbstractUnivariateSolver

protected BaseAbstractUnivariateSolver(double relativeAccuracy,
                                       double absoluteAccuracy)

Construct a solver with given accuracies.

Parameters:

relativeAccuracy - Maximum relative error.

absoluteAccuracy - Maximum absolute error.

BaseAbstractUnivariateSolver

protected BaseAbstractUnivariateSolver(double relativeAccuracy,
                                       double absoluteAccuracy,
                                       double functionValueAccuracy)

Construct a solver with given accuracies.

Parameters:

relativeAccuracy - Maximum relative error.

absoluteAccuracy - Maximum absolute error.

functionValueAccuracy - Maximum function value error.

Method Detail

getMaxEvaluations

public int getMaxEvaluations()

Get the maximum number of function evaluations.

Specified by:

getMaxEvaluations in interface BaseUnivariateSolver<FUNC extends UnivariateFunction>

Returns:

the maximum number of function evaluations.

getEvaluations

public int getEvaluations()

Get the number of evaluations of the objective function. The number of evaluations corresponds to the last call to the optimize method. It is 0 if the method has not been called yet.

Specified by:

getEvaluations in interface BaseUnivariateSolver<FUNC extends UnivariateFunction>

Returns:

the number of evaluations of the objective function.

getMin

public double getMin()

Returns:

the lower end of the search interval.

getMax

public double getMax()

Returns:

the higher end of the search interval.

getStartValue

public double getStartValue()

Returns:

the initial guess.

getAbsoluteAccuracy

public double getAbsoluteAccuracy()

Get the absolute accuracy of the solver. Solutions returned by the solver should be accurate to this tolerance, i.e., if ε is the absolute accuracy of the solver and v is a value returned by one of the solve methods, then a root of the function should exist somewhere in the interval (v - ε, v + ε).

Specified by:

getAbsoluteAccuracy in interface BaseUnivariateSolver<FUNC extends UnivariateFunction>

Returns:

the absolute accuracy.

getRelativeAccuracy

public double getRelativeAccuracy()

Get the relative accuracy of the solver. The contract for relative accuracy is the same as BaseUnivariateSolver.getAbsoluteAccuracy(), but using relative, rather than absolute error. If ρ is the relative accuracy configured for a solver and v is a value returned, then a root of the function should exist somewhere in the interval (v - ρ v, v + ρ v).

Specified by:

getRelativeAccuracy in interface BaseUnivariateSolver<FUNC extends UnivariateFunction>

Returns:

the relative accuracy.

getFunctionValueAccuracy

public double getFunctionValueAccuracy()

Get the function value accuracy of the solver. If v is a value returned by the solver for a function f, then by contract, |f(v)| should be less than or equal to the function value accuracy configured for the solver.

Specified by:

getFunctionValueAccuracy in interface BaseUnivariateSolver<FUNC extends UnivariateFunction>

Returns:

the function value accuracy.

computeObjectiveValue

protected double computeObjectiveValue(double point)

Compute the objective function value.

Parameters:

point - Point at which the objective function must be evaluated.

Returns:

the objective function value at specified point.

Throws:

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

setup

protected void setup(int maxEval,
                     FUNC f,
                     double min,
                     double max,
                     double startValue)

Prepare for computation. Subclasses must call this method if they override any of the solve methods.

Parameters:

f - Function to solve.

min - Lower bound for the interval.

max - Upper bound for the interval.

startValue - Start value to use.

maxEval - Maximum number of evaluations.

Throws:

NullArgumentException - if f is null.

solve

public double solve(int maxEval,
                    FUNC 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<FUNC extends 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.

solve

public double solve(int maxEval,
                    FUNC f,
                    double min,
                    double max)

Solve for a zero root 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 BaseUnivariateSolver<FUNC extends UnivariateFunction>

Parameters:

maxEval - Maximum number of evaluations.

f - Function to solve.

min - Lower bound for the interval.

max - Upper bound for the interval.

Returns:

a value where the function is zero.

solve

public double solve(int maxEval,
                    FUNC f,
                    double startValue)

Solve for a zero in the vicinity of startValue.

Specified by:

solve in interface BaseUnivariateSolver<FUNC extends UnivariateFunction>

Parameters:

maxEval - Maximum number of evaluations.

f - Function to solve.

startValue - Start value to use.

Returns:

a value where the function is zero.

doSolve

protected abstract double doSolve()

Method for implementing actual optimization algorithms in derived classes.

Returns:

the root.

Throws:

TooManyEvaluationsException - if the maximal number of evaluations is exceeded.

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

isBracketing

protected boolean isBracketing(double lower,
                               double upper)

Check whether the function takes opposite signs at the endpoints.

Parameters:

lower - Lower endpoint.

upper - Upper endpoint.

Returns:

true if the function values have opposite signs at the given points.

isSequence

protected boolean isSequence(double start,
                             double mid,
                             double end)

Check whether the arguments form a (strictly) increasing sequence.

Parameters:

start - First number.

mid - Second number.

end - Third number.

Returns:

true if the arguments form an increasing sequence.

verifyInterval

protected void verifyInterval(double lower,
                              double upper)

Check that the endpoints specify an interval.

Parameters:

lower - Lower endpoint.

upper - Upper endpoint.

Throws:

NumberIsTooLargeException - if lower >= upper.

verifySequence

protected void verifySequence(double lower,
                              double initial,
                              double upper)

Check that lower < initial < upper.

Parameters:

lower - Lower endpoint.

initial - Initial value.

upper - Upper endpoint.

Throws:

NumberIsTooLargeException - if lower >= initial or initial >= upper.

verifyBracketing

protected void verifyBracketing(double lower,
                                double upper)

Check that the endpoints specify an interval and the function takes opposite signs at the endpoints.

Parameters:

lower - Lower endpoint.

upper - Upper endpoint.

Throws:

NullArgumentException - if the function has not been set.

NoBracketingException - if the function has the same sign at the endpoints.

incrementEvaluationCount

protected void incrementEvaluationCount()

Increment the evaluation count by one. Method computeObjectiveValue(double) calls this method internally. It is provided for subclasses that do not exclusively use computeObjectiveValue to solve the function. See e.g. AbstractUnivariateDifferentiableSolver.

Throws:

TooManyEvaluationsException - when the allowed number of function evaluations has been exhausted.