org.apache.commons.math3.dfp

Class BracketingNthOrderBrentSolverDFP

java.lang.Object

org.apache.commons.math3.dfp.BracketingNthOrderBrentSolverDFP

public class BracketingNthOrderBrentSolverDFP
extends java.lang.Object

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.

Field Summary

Fields

Modifier and Type	Field and Description
private Dfp	absoluteAccuracy Absolute accuracy.
private Incrementor	evaluations Evaluations counter.
private Dfp	functionValueAccuracy Function value accuracy.
private static int	MAXIMAL_AGING Maximal aging triggering an attempt to balance the bracketing interval.
private int	maximalOrder Maximal order.
private Dfp	relativeAccuracy Relative accuracy.

Constructor Summary

Constructors

Constructor and Description
BracketingNthOrderBrentSolverDFP(Dfp relativeAccuracy, Dfp absoluteAccuracy, Dfp functionValueAccuracy, int maximalOrder) Construct a solver.

Method Summary

Methods

Modifier and Type	Method and Description
Dfp	getAbsoluteAccuracy() Get the absolute accuracy.
int	getEvaluations() Get the number of evaluations of the objective function.
Dfp	getFunctionValueAccuracy() Get the function accuracy.
int	getMaxEvaluations() Get the maximal number of function evaluations.
int	getMaximalOrder() Get the maximal order.
Dfp	getRelativeAccuracy() Get the relative accuracy.
private Dfp	guessX(Dfp targetY, Dfp[] x, Dfp[] y, int start, int end) Guess an x value by nth order inverse polynomial interpolation.
Dfp	solve(int maxEval, UnivariateDfpFunction f, Dfp min, Dfp max, AllowedSolution allowedSolution) Solve for a zero in the given interval.
Dfp	solve(int maxEval, UnivariateDfpFunction f, Dfp min, Dfp max, Dfp startValue, AllowedSolution allowedSolution) Solve for a zero in the given interval, start at startValue.

Methods inherited from class java.lang.Object

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

Field Detail

MAXIMAL_AGING

private static final int MAXIMAL_AGING

Maximal aging triggering an attempt to balance the bracketing interval.

See Also:

Constant Field Values

maximalOrder

private final int maximalOrder

Maximal order.

functionValueAccuracy

private final Dfp functionValueAccuracy

Function value accuracy.

absoluteAccuracy

private final Dfp absoluteAccuracy

Absolute accuracy.

relativeAccuracy

private final Dfp relativeAccuracy

Relative accuracy.

evaluations

private final Incrementor evaluations

Evaluations counter.

Constructor Detail

BracketingNthOrderBrentSolverDFP

public BracketingNthOrderBrentSolverDFP(Dfp relativeAccuracy,
                                Dfp absoluteAccuracy,
                                Dfp functionValueAccuracy,
                                int maximalOrder)
                                 throws NumberIsTooSmallException

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

functionValueAccuracy - Function value accuracy.

maximalOrder - maximal order.

Throws:

NumberIsTooSmallException - if maximal order is lower than 2

Method Detail

getMaximalOrder

public int getMaximalOrder()

Get the maximal order.

Returns:

maximal order

getMaxEvaluations

public int getMaxEvaluations()

Get the maximal number of function evaluations.

Returns:

the maximal 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.

Returns:

the number of evaluations of the objective function.

getAbsoluteAccuracy

public Dfp getAbsoluteAccuracy()

Get the absolute accuracy.

Returns:

absolute accuracy

getRelativeAccuracy

public Dfp getRelativeAccuracy()

Get the relative accuracy.

Returns:

relative accuracy

getFunctionValueAccuracy

public Dfp getFunctionValueAccuracy()

Get the function accuracy.

Returns:

function accuracy

solve

public Dfp solve(int maxEval,
        UnivariateDfpFunction f,
        Dfp min,
        Dfp max,
        AllowedSolution allowedSolution)
          throws NullArgumentException,
                 NoBracketingException

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 - 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:

NullArgumentException - if f is null.

NoBracketingException - if root cannot be bracketed

solve

public Dfp solve(int maxEval,
        UnivariateDfpFunction f,
        Dfp min,
        Dfp max,
        Dfp startValue,
        AllowedSolution allowedSolution)
          throws NullArgumentException,
                 NoBracketingException

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 - 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:

NullArgumentException - if f is null.

NoBracketingException - if root cannot be bracketed

guessX

private Dfp guessX(Dfp targetY,
         Dfp[] x,
         Dfp[] y,
         int start,
         int end)

Guess an x value by n^th order inverse polynomial interpolation.

The x value is guessed by evaluating polynomial Q(y) at y = targetY, where Q is built such that for all considered points (x_i, y_i), Q(y_i) = x_i.

Parameters:

targetY - target value for y

x - reference points abscissas for interpolation, note that this array is modified during computation

y - reference points ordinates for interpolation

start - start index of the points to consider (inclusive)

end - end index of the points to consider (exclusive)

Returns:

guessed root (will be a NaN if two points share the same y)