Class BracketingNthOrderBrentSolver
- java.lang.Object
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- org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<UnivariateFunction>
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- org.apache.commons.math3.analysis.solvers.AbstractUnivariateSolver
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- org.apache.commons.math3.analysis.solvers.BracketingNthOrderBrentSolver
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- 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.
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Field Summary
Fields Modifier and Type Field Description private AllowedSolution
allowed
The kinds of solutions that the algorithm may accept.private static double
DEFAULT_ABSOLUTE_ACCURACY
Default absolute accuracy.private static int
DEFAULT_MAXIMAL_ORDER
Default maximal order.private static int
MAXIMAL_AGING
Maximal aging triggering an attempt to balance the bracketing interval.private int
maximalOrder
Maximal order.private static double
REDUCTION_FACTOR
Reduction factor for attempts to balance the bracketing interval.
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Constructor Summary
Constructors Constructor 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.
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Method Summary
All Methods Instance Methods Concrete Methods Modifier and Type Method Description protected double
doSolve()
Method for implementing actual optimization algorithms in derived classes.int
getMaximalOrder()
Get the maximal order.private double
guessX(double targetY, double[] x, double[] y, int start, int end)
Guess an x value by nth order inverse polynomial interpolation.double
solve(int maxEval, UnivariateFunction f, double min, double max, double startValue, AllowedSolution allowedSolution)
Solve for a zero in the given interval, start atstartValue
.double
solve(int maxEval, UnivariateFunction f, double min, double max, AllowedSolution allowedSolution)
Solve for a zero in the given interval.-
Methods inherited from class org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver
computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, getMaxEvaluations, getMin, getRelativeAccuracy, getStartValue, incrementEvaluationCount, isBracketing, isSequence, setup, solve, solve, solve, verifyBracketing, verifyInterval, verifySequence
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Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
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Methods inherited from interface org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver
getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMaxEvaluations, getRelativeAccuracy, solve, solve, solve
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Field Detail
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DEFAULT_ABSOLUTE_ACCURACY
private static final double DEFAULT_ABSOLUTE_ACCURACY
Default absolute accuracy.- See Also:
- Constant Field Values
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DEFAULT_MAXIMAL_ORDER
private static final int DEFAULT_MAXIMAL_ORDER
Default maximal order.- See Also:
- Constant Field Values
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MAXIMAL_AGING
private static final int MAXIMAL_AGING
Maximal aging triggering an attempt to balance the bracketing interval.- See Also:
- Constant Field Values
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REDUCTION_FACTOR
private static final double REDUCTION_FACTOR
Reduction factor for attempts to balance the bracketing interval.- See Also:
- Constant Field Values
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maximalOrder
private final int maximalOrder
Maximal order.
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allowed
private AllowedSolution allowed
The kinds of solutions that the algorithm may accept.
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Constructor Detail
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BracketingNthOrderBrentSolver
public BracketingNthOrderBrentSolver()
Construct a solver with default accuracy and maximal order (1e-6 and 5 respectively)
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BracketingNthOrderBrentSolver
public BracketingNthOrderBrentSolver(double absoluteAccuracy, int maximalOrder) throws NumberIsTooSmallException
Construct a solver.- Parameters:
absoluteAccuracy
- Absolute accuracy.maximalOrder
- maximal order.- Throws:
NumberIsTooSmallException
- if maximal order is lower than 2
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BracketingNthOrderBrentSolver
public BracketingNthOrderBrentSolver(double relativeAccuracy, double absoluteAccuracy, int maximalOrder) throws NumberIsTooSmallException
Construct a solver.- Parameters:
relativeAccuracy
- Relative accuracy.absoluteAccuracy
- Absolute accuracy.maximalOrder
- maximal order.- Throws:
NumberIsTooSmallException
- if maximal order is lower than 2
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BracketingNthOrderBrentSolver
public BracketingNthOrderBrentSolver(double relativeAccuracy, double absoluteAccuracy, double 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
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Method Detail
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getMaximalOrder
public int getMaximalOrder()
Get the maximal order.- Returns:
- maximal order
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doSolve
protected double doSolve() throws TooManyEvaluationsException, NumberIsTooLargeException, NoBracketingException
Method for implementing actual optimization algorithms in derived classes.- Specified by:
doSolve
in classBaseAbstractUnivariateSolver<UnivariateFunction>
- 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.NumberIsTooLargeException
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guessX
private double guessX(double targetY, double[] x, double[] y, int start, int end)
Guess an x value by nth 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 (xi, yi), Q(yi) = xi.
- Parameters:
targetY
- target value for yx
- reference points abscissas for interpolation, note that this array is modified during computationy
- reference points ordinates for interpolationstart
- 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)
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solve
public double solve(int maxEval, UnivariateFunction f, double min, double max, AllowedSolution allowedSolution) throws TooManyEvaluationsException, NumberIsTooLargeException, 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 interfaceBracketedUnivariateSolver<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:
TooManyEvaluationsException
- if the allowed number of evaluations is exceeded.NumberIsTooLargeException
NoBracketingException
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solve
public double solve(int maxEval, UnivariateFunction f, double min, double max, double startValue, AllowedSolution allowedSolution) throws TooManyEvaluationsException, NumberIsTooLargeException, NoBracketingException
Solve for a zero in the given interval, start atstartValue
. 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 interfaceBracketedUnivariateSolver<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:
TooManyEvaluationsException
- if the allowed number of evaluations is exceeded.NumberIsTooLargeException
NoBracketingException
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