Class MullerSolver
- 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.MullerSolver
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- All Implemented Interfaces:
BaseUnivariateSolver<UnivariateFunction>
,UnivariateSolver
public class MullerSolver extends AbstractUnivariateSolver
This class implements the Muller's Method for root finding of real univariate functions. For reference, see Elementary Numerical Analysis, ISBN 0070124477, chapter 3.Muller's method applies to both real and complex functions, but here we restrict ourselves to real functions. This class differs from
MullerSolver
in the way it avoids complex operations.Muller's original method would have function evaluation at complex point. Since our f(x) is real, we have to find ways to avoid that. Bracketing condition is one way to go: by requiring bracketing in every iteration, the newly computed approximation is guaranteed to be real.
Normally Muller's method converges quadratically in the vicinity of a zero, however it may be very slow in regions far away from zeros. For example, f(x) = exp(x) - 1, min = -50, max = 100. In such case we use bisection as a safety backup if it performs very poorly.
The formulas here use divided differences directly.
- Since:
- 1.2
- See Also:
MullerSolver2
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Field Summary
Fields Modifier and Type Field Description private static double
DEFAULT_ABSOLUTE_ACCURACY
Default absolute accuracy.
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Constructor Summary
Constructors Constructor Description MullerSolver()
Construct a solver with default accuracy (1e-6).MullerSolver(double absoluteAccuracy)
Construct a solver.MullerSolver(double relativeAccuracy, double absoluteAccuracy)
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.private double
solve(double min, double max, double fMin, double fMax)
Find a real root 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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Constructor Detail
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MullerSolver
public MullerSolver()
Construct a solver with default accuracy (1e-6).
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MullerSolver
public MullerSolver(double absoluteAccuracy)
Construct a solver.- Parameters:
absoluteAccuracy
- Absolute accuracy.
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MullerSolver
public MullerSolver(double relativeAccuracy, double absoluteAccuracy)
Construct a solver.- Parameters:
relativeAccuracy
- Relative accuracy.absoluteAccuracy
- Absolute accuracy.
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Method Detail
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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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solve
private double solve(double min, double max, double fMin, double fMax) throws TooManyEvaluationsException
Find a real root in the given interval.- Parameters:
min
- Lower bound for the interval.max
- Upper bound for the interval.fMin
- function value at the lower bound.fMax
- function value at the upper bound.- Returns:
- the point at which the function value is zero.
- Throws:
TooManyEvaluationsException
- if the allowed number of calls to the function to be solved has been exhausted.
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