Package org.apache.commons.math.analysis.solvers

Class MullerSolver

java.lang.Object

org.apache.commons.math.ConvergingAlgorithmImpl

org.apache.commons.math.analysis.solvers.UnivariateRealSolverImpl

org.apache.commons.math.analysis.solvers.MullerSolver

All Implemented Interfaces:

UnivariateRealSolver, ConvergingAlgorithm

public class MullerSolver
extends UnivariateRealSolverImpl

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. Methods solve() and solve2() find real zeros, using different ways to bypass complex arithmetics.

Since:

1.2

Constructor Summary

Constructors

Constructor	Description
MullerSolver()	Deprecated. in 2.2 (to be removed in 3.0).
MullerSolver(UnivariateRealFunction f)	Deprecated. as of 2.0 the function to solve is passed as an argument to the solve(UnivariateRealFunction, double, double) or UnivariateRealSolver.solve(UnivariateRealFunction, double, double, double) method.

Method Summary

Modifier and Type	Method	Description
double	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 by solve2(UnivariateRealFunction, double, double) since 2.0
double	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

getFunctionValue, getFunctionValueAccuracy, getResult, resetFunctionValueAccuracy, setFunctionValueAccuracy

Methods inherited from class org.apache.commons.math.ConvergingAlgorithmImpl

getAbsoluteAccuracy, getIterationCount, getMaximalIterationCount, getRelativeAccuracy, resetAbsoluteAccuracy, resetMaximalIterationCount, resetRelativeAccuracy, setAbsoluteAccuracy, setMaximalIterationCount, setRelativeAccuracy

Methods inherited from class java.lang.Object

equals, 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

Constructor Detail

MullerSolver

@Deprecated
public MullerSolver(UnivariateRealFunction f)

Deprecated.

as of 2.0 the function to solve is passed as an argument to the solve(UnivariateRealFunction, double, double) or UnivariateRealSolver.solve(UnivariateRealFunction, double, double, double) method.

Construct a solver for the given function.

Parameters:

f - function to solve

MullerSolver

@Deprecated
public MullerSolver()

Deprecated.

in 2.2 (to be removed in 3.0).

Construct a solver.

Method Detail

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

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

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 class UnivariateRealSolverImpl

Parameters:

f - the function to solve

min - the lower bound for the interval

max - the upper bound for the interval

initial - the start value to use

maxEval - 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 otherwise

FunctionEvaluationException - if an error occurs evaluating the function

java.lang.IllegalArgumentException - if any parameters are invalid

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 solve

min - the lower bound for the interval

max - the upper bound for the interval

initial - 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 otherwise

FunctionEvaluationException - if an error occurs evaluating the function

java.lang.IllegalArgumentException - if any parameters are invalid

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 class UnivariateRealSolverImpl

Parameters:

f - the function to solve

min - the lower bound for the interval

max - the upper bound for the interval

maxEval - 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 otherwise

FunctionEvaluationException - if an error occurs evaluating the function

java.lang.IllegalArgumentException - if any parameters are invalid

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 solve

min - the lower bound for the interval

max - 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 otherwise

FunctionEvaluationException - if an error occurs evaluating the function

java.lang.IllegalArgumentException - if any parameters are invalid

solve2

@Deprecated
public double solve2(double min,
                     double max)
              throws MaxIterationsExceededException,
                     FunctionEvaluationException

Deprecated.

replaced by solve2(UnivariateRealFunction, double, double) since 2.0

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:

min - the lower bound for the interval

max - 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 otherwise

FunctionEvaluationException - if an error occurs evaluating the function

java.lang.IllegalArgumentException - if any parameters are invalid

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 solve

min - the lower bound for the interval

max - 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 otherwise

FunctionEvaluationException - if an error occurs evaluating the function

java.lang.IllegalArgumentException - if any parameters are invalid