org.apache.commons.math3.analysis.solvers

Class FieldBracketingNthOrderBrentSolver<T extends RealFieldElement<T>>

java.lang.Object

org.apache.commons.math3.analysis.solvers.FieldBracketingNthOrderBrentSolver<T>

Type Parameters:

T - the type of the field elements

All Implemented Interfaces:

BracketedRealFieldUnivariateSolver<T>

Direct Known Subclasses:

BracketingNthOrderBrentSolverDFP

public class FieldBracketingNthOrderBrentSolver<T extends RealFieldElement<T>>
extends java.lang.Object
implements BracketedRealFieldUnivariateSolver<T>

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.

Since:

3.6

Field Summary

Fields

Modifier and Type	Field and Description
private T	absoluteAccuracy Absolute accuracy.
private IntegerSequence.Incrementor	evaluations Evaluations counter.
private Field<T>	field Field to which the elements belong.
private T	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 T	relativeAccuracy Relative accuracy.

Constructor Summary

Constructors

Constructor and Description
FieldBracketingNthOrderBrentSolver(T relativeAccuracy, T absoluteAccuracy, T functionValueAccuracy, int maximalOrder) Construct a solver.

Method Summary

Methods

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

field

private final Field<T extends RealFieldElement<T>> field

Field to which the elements belong.

maximalOrder

private final int maximalOrder

Maximal order.

functionValueAccuracy

private final T extends RealFieldElement<T> functionValueAccuracy

Function value accuracy.

absoluteAccuracy

private final T extends RealFieldElement<T> absoluteAccuracy

Absolute accuracy.

relativeAccuracy

private final T extends RealFieldElement<T> relativeAccuracy

Relative accuracy.

evaluations

private IntegerSequence.Incrementor evaluations

Evaluations counter.

Constructor Detail

FieldBracketingNthOrderBrentSolver

public FieldBracketingNthOrderBrentSolver(T relativeAccuracy,
                                  T absoluteAccuracy,
                                  T 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.

Specified by:

getMaxEvaluations in interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>>

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.

Specified by:

getEvaluations in interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>>

Returns:

the number of evaluations of the objective function.

getAbsoluteAccuracy

public T getAbsoluteAccuracy()

Get the absolute accuracy.

Specified by:

getAbsoluteAccuracy in interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>>

Returns:

absolute accuracy

getRelativeAccuracy

public T getRelativeAccuracy()

Get the relative accuracy.

Specified by:

getRelativeAccuracy in interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>>

Returns:

relative accuracy

getFunctionValueAccuracy

public T getFunctionValueAccuracy()

Get the function accuracy.

Specified by:

getFunctionValueAccuracy in interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>>

Returns:

function accuracy

solve

public T solve(int maxEval,
      RealFieldUnivariateFunction<T> f,
      T min,
      T 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.

Specified by:

solve in interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>>

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 T solve(int maxEval,
      RealFieldUnivariateFunction<T> f,
      T min,
      T max,
      T 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.

Specified by:

solve in interface BracketedRealFieldUnivariateSolver<T extends RealFieldElement<T>>

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 T guessX(T targetY,
       T[] x,
       T[] 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)