Class BracketingNthOrderBrentSolver
java.lang.Object
org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<UnivariateFunction>
org.apache.commons.math3.analysis.solvers.AbstractUnivariateSolver
org.apache.commons.math3.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.
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Field Summary
FieldsModifier and TypeFieldDescriptionprivate AllowedSolution
The kinds of solutions that the algorithm may accept.private static final double
Default absolute accuracy.private static final int
Default maximal order.private static final int
Maximal aging triggering an attempt to balance the bracketing interval.private final int
Maximal order.private static final double
Reduction factor for attempts to balance the bracketing interval. -
Constructor Summary
ConstructorsConstructorDescriptionConstruct 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 TypeMethodDescriptionprotected double
doSolve()
Method for implementing actual optimization algorithms in derived classes.int
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
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
Methods inherited from interface org.apache.commons.math3.analysis.solvers.BaseUnivariateSolver
getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMaxEvaluations, getRelativeAccuracy, solve, solve, solve
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Field Details
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DEFAULT_ABSOLUTE_ACCURACY
private static final double DEFAULT_ABSOLUTE_ACCURACYDefault absolute accuracy.- See Also:
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DEFAULT_MAXIMAL_ORDER
private static final int DEFAULT_MAXIMAL_ORDERDefault maximal order.- See Also:
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MAXIMAL_AGING
private static final int MAXIMAL_AGINGMaximal aging triggering an attempt to balance the bracketing interval.- See Also:
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REDUCTION_FACTOR
private static final double REDUCTION_FACTORReduction factor for attempts to balance the bracketing interval.- See Also:
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maximalOrder
private final int maximalOrderMaximal order. -
allowed
The kinds of solutions that the algorithm may accept.
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Constructor Details
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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 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 Details
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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, NoBracketingExceptionMethod 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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