Class MullerSolver
- All Implemented Interfaces:
UnivariateRealSolver
,ConvergingAlgorithm
Muller's method applies to both real and complex functions, but here we restrict ourselves to real functions. Methods solve() and solve2() find real zeros, using different ways to bypass complex arithmetics.
- Since:
- 1.2
- Version:
- $Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $
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Field Summary
Fields inherited from class org.apache.commons.math.analysis.solvers.UnivariateRealSolverImpl
defaultFunctionValueAccuracy, f, functionValue, functionValueAccuracy, result, resultComputed
Fields inherited from class org.apache.commons.math.ConvergingAlgorithmImpl
absoluteAccuracy, defaultAbsoluteAccuracy, defaultMaximalIterationCount, defaultRelativeAccuracy, iterationCount, maximalIterationCount, relativeAccuracy
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Constructor Summary
ConstructorsConstructorDescriptionDeprecated.in 2.2 (to be removed in 3.0).Deprecated.as of 2.0 the function to solve is passed as an argument to thesolve(UnivariateRealFunction, double, double)
orUnivariateRealSolver.solve(UnivariateRealFunction, double, double, double)
method. -
Method Summary
Modifier and TypeMethodDescriptiondouble
solve
(double min, double max) Deprecated.double
solve
(double min, double max, double initial) Deprecated.double
solve
(int maxEval, UnivariateRealFunction f, double min, double max) Find a real root in the given interval.double
solve
(int maxEval, UnivariateRealFunction f, double min, double max, double initial) Find a real root in the given interval with initial value.double
solve
(UnivariateRealFunction f, double min, double max) Deprecated.in 2.2 (to be removed in 3.0).double
solve
(UnivariateRealFunction f, double min, double max, double initial) Deprecated.in 2.2 (to be removed in 3.0).double
solve2
(double min, double max) Deprecated.replaced bysolve2(UnivariateRealFunction, double, double)
since 2.0double
solve2
(UnivariateRealFunction f, double min, double max) Deprecated.in 2.2 (to be removed in 3.0).Methods inherited from class org.apache.commons.math.analysis.solvers.UnivariateRealSolverImpl
checkResultComputed, clearResult, getFunctionValue, getFunctionValueAccuracy, getResult, isBracketing, isSequence, resetFunctionValueAccuracy, setFunctionValueAccuracy, setResult, setResult, verifyBracketing, verifyInterval, verifySequence
Methods inherited from class org.apache.commons.math.ConvergingAlgorithmImpl
getAbsoluteAccuracy, getIterationCount, getMaximalIterationCount, getRelativeAccuracy, incrementIterationsCounter, resetAbsoluteAccuracy, resetIterationsCounter, resetMaximalIterationCount, resetRelativeAccuracy, setAbsoluteAccuracy, setMaximalIterationCount, setRelativeAccuracy
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.math.ConvergingAlgorithm
getAbsoluteAccuracy, getIterationCount, getMaximalIterationCount, getRelativeAccuracy, resetAbsoluteAccuracy, resetMaximalIterationCount, resetRelativeAccuracy, setAbsoluteAccuracy, setMaximalIterationCount, setRelativeAccuracy
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Constructor Details
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MullerSolver
Deprecated.as of 2.0 the function to solve is passed as an argument to thesolve(UnivariateRealFunction, double, double)
orUnivariateRealSolver.solve(UnivariateRealFunction, double, double, double)
method.Construct a solver for the given function.- Parameters:
f
- function to solve
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MullerSolver
Deprecated.in 2.2 (to be removed in 3.0).Construct a solver.
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Method Details
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solve
@Deprecated public double solve(double min, double max) throws ConvergenceException, FunctionEvaluationException Deprecated.Solve for a zero root 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:
min
- the lower bound for the interval.max
- the upper bound for the interval.- Returns:
- a value where the function is zero
- Throws:
ConvergenceException
- if the maximum iteration count is exceeded or the solver detects convergence problems otherwise.FunctionEvaluationException
- if an error occurs evaluating the function
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solve
@Deprecated public double solve(double min, double max, double initial) throws ConvergenceException, FunctionEvaluationException Deprecated.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:
min
- the lower bound for the interval.max
- the upper bound for the interval.initial
- the start value to use- Returns:
- a value where the function is zero
- Throws:
ConvergenceException
- if the maximum iteration count is exceeded or the solver detects convergence problems otherwise.FunctionEvaluationException
- if an error occurs evaluating the function
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solve
public double solve(int maxEval, UnivariateRealFunction f, double min, double max, double initial) throws MaxIterationsExceededException, FunctionEvaluationException Find a real root in the given interval with initial value.Requires bracketing condition.
- Overrides:
solve
in classUnivariateRealSolverImpl
- Parameters:
f
- the function to solvemin
- the lower bound for the intervalmax
- the upper bound for the intervalinitial
- the start value to usemaxEval
- Maximum number of evaluations.- Returns:
- the point at which the function value is zero
- Throws:
MaxIterationsExceededException
- if the maximum iteration count is exceeded or the solver detects convergence problems otherwiseFunctionEvaluationException
- if an error occurs evaluating the functionIllegalArgumentException
- if any parameters are invalid
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solve
@Deprecated public double solve(UnivariateRealFunction f, double min, double max, double initial) throws MaxIterationsExceededException, FunctionEvaluationException Deprecated.in 2.2 (to be removed in 3.0).Find a real root in the given interval with initial value.Requires bracketing condition.
- Parameters:
f
- the function to solvemin
- the lower bound for the intervalmax
- the upper bound for the intervalinitial
- the start value to use- Returns:
- the point at which the function value is zero
- Throws:
MaxIterationsExceededException
- if the maximum iteration count is exceeded or the solver detects convergence problems otherwiseFunctionEvaluationException
- if an error occurs evaluating the functionIllegalArgumentException
- if any parameters are invalid
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solve
public double solve(int maxEval, UnivariateRealFunction f, double min, double max) throws MaxIterationsExceededException, FunctionEvaluationException Find a real root in the given interval.Original Muller's 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.
- Overrides:
solve
in classUnivariateRealSolverImpl
- Parameters:
f
- the function to solvemin
- the lower bound for the intervalmax
- the upper bound for the intervalmaxEval
- Maximum number of evaluations.- Returns:
- the point at which the function value is zero
- Throws:
MaxIterationsExceededException
- if the maximum iteration count is exceeded or the solver detects convergence problems otherwiseFunctionEvaluationException
- if an error occurs evaluating the functionIllegalArgumentException
- if any parameters are invalid
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solve
@Deprecated public double solve(UnivariateRealFunction f, double min, double max) throws MaxIterationsExceededException, FunctionEvaluationException Deprecated.in 2.2 (to be removed in 3.0).Find a real root in the given interval.Original Muller's 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.
- Parameters:
f
- the function to solvemin
- the lower bound for the intervalmax
- the upper bound for the interval- Returns:
- the point at which the function value is zero
- Throws:
MaxIterationsExceededException
- if the maximum iteration count is exceeded or the solver detects convergence problems otherwiseFunctionEvaluationException
- if an error occurs evaluating the functionIllegalArgumentException
- if any parameters are invalid
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solve2
@Deprecated public double solve2(double min, double max) throws MaxIterationsExceededException, FunctionEvaluationException Deprecated.replaced bysolve2(UnivariateRealFunction, double, double)
since 2.0Find a real root in the given interval.solve2() differs from solve() in the way it avoids complex operations. Except for the initial [min, max], solve2() does not require bracketing condition, e.g. f(x0), f(x1), f(x2) can have the same sign. If complex number arises in the computation, we simply use its modulus as real approximation.
Because the interval may not be bracketing, bisection alternative is not applicable here. However in practice our treatment usually works well, especially near real zeros where the imaginary part of complex approximation is often negligible.
The formulas here do not use divided differences directly.
- Parameters:
min
- the lower bound for the intervalmax
- the upper bound for the interval- Returns:
- the point at which the function value is zero
- Throws:
MaxIterationsExceededException
- if the maximum iteration count is exceeded or the solver detects convergence problems otherwiseFunctionEvaluationException
- if an error occurs evaluating the functionIllegalArgumentException
- if any parameters are invalid
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solve2
@Deprecated public double solve2(UnivariateRealFunction f, double min, double max) throws MaxIterationsExceededException, FunctionEvaluationException Deprecated.in 2.2 (to be removed in 3.0).Find a real root in the given interval.solve2() differs from solve() in the way it avoids complex operations. Except for the initial [min, max], solve2() does not require bracketing condition, e.g. f(x0), f(x1), f(x2) can have the same sign. If complex number arises in the computation, we simply use its modulus as real approximation.
Because the interval may not be bracketing, bisection alternative is not applicable here. However in practice our treatment usually works well, especially near real zeros where the imaginary part of complex approximation is often negligible.
The formulas here do not use divided differences directly.
- Parameters:
f
- the function to solvemin
- the lower bound for the intervalmax
- the upper bound for the interval- Returns:
- the point at which the function value is zero
- Throws:
MaxIterationsExceededException
- if the maximum iteration count is exceeded or the solver detects convergence problems otherwiseFunctionEvaluationException
- if an error occurs evaluating the functionIllegalArgumentException
- if any parameters are invalid
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