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

java.lang.Object
  extended by org.apache.commons.math.ConvergingAlgorithmImpl
      extended by org.apache.commons.math.analysis.solvers.UnivariateRealSolverImpl
          extended by 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
Version:
$Revision: 1070725 $ $Date: 2011-02-15 02:31:12 +0100 (mar. 15 févr. 2011) $

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
 
Constructor Summary
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
 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
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
 

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


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