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

Class LaguerreSolver

java.lang.Object

org.apache.commons.math.ConvergingAlgorithmImpl

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

org.apache.commons.math.analysis.solvers.LaguerreSolver

All Implemented Interfaces:

UnivariateRealSolver, ConvergingAlgorithm

public class LaguerreSolver
extends UnivariateRealSolverImpl

Implements the Laguerre's Method for root finding of real coefficient polynomials. For reference, see A First Course in Numerical Analysis, ISBN 048641454X, chapter 8.

Laguerre's method is global in the sense that it can start with any initial approximation and be able to solve all roots from that point.

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

Constructors

Constructor	Description
LaguerreSolver()	Deprecated. in 2.2 (to be removed in 3.0)
LaguerreSolver(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
PolynomialFunction	getPolynomialFunction()	Deprecated. as of 2.0 the function is not stored anymore within the instance.
protected boolean	isRootOK(double min, double max, Complex z)	Returns true iff the given complex root is actually a real zero in the given interval, within the solver tolerance level.
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).
Complex	solve(Complex[] coefficients, Complex initial)	Deprecated. in 2.2.
Complex[]	solveAll(double[] coefficients, double initial)	Deprecated. in 2.2.
Complex[]	solveAll(Complex[] coefficients, Complex initial)	Deprecated. in 2.2.

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

LaguerreSolver

@Deprecated
public LaguerreSolver(UnivariateRealFunction f)
               throws java.lang.IllegalArgumentException

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

Throws:

java.lang.IllegalArgumentException - if function is not polynomial

LaguerreSolver

@Deprecated
public LaguerreSolver()

Deprecated.

in 2.2 (to be removed in 3.0)

Construct a solver.

Method Detail

getPolynomialFunction

@Deprecated
public PolynomialFunction getPolynomialFunction()

Deprecated.

as of 2.0 the function is not stored anymore within the instance.

Returns a copy of the polynomial function.

Returns:

a fresh copy of the polynomial function

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 ConvergenceException,
                    FunctionEvaluationException

Find a real root in the given interval with initial value.

Requires bracketing condition.

Overrides:

solve in class UnivariateRealSolverImpl

Parameters:

f - function to solve (must be polynomial)

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:

ConvergenceException - 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 ConvergenceException,
                    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 - function to solve (must be polynomial)

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:

ConvergenceException - 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 ConvergenceException,
                    FunctionEvaluationException

Find a real root in the given interval.

Despite the bracketing condition, the root returned by solve(Complex[], Complex) may not be a real zero inside [min, max]. For example, p(x) = x^3 + 1, min = -2, max = 2, initial = 0. We can either try another initial value, or, as we did here, call solveAll() to obtain all roots and pick up the one that we're looking for.

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:

ConvergenceException - 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 ConvergenceException,
                    FunctionEvaluationException

Deprecated.

in 2.2 (to be removed in 3.0).

Find a real root in the given interval.

Despite the bracketing condition, the root returned by solve(Complex[], Complex) may not be a real zero inside [min, max]. For example, p(x) = x^3 + 1, min = -2, max = 2, initial = 0. We can either try another initial value, or, as we did here, call solveAll() to obtain all roots and pick up the one that we're looking for.

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:

ConvergenceException - 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

isRootOK

protected boolean isRootOK(double min,
                           double max,
                           Complex z)

Returns true iff the given complex root is actually a real zero in the given interval, within the solver tolerance level.

Parameters:

min - the lower bound for the interval

max - the upper bound for the interval

z - the complex root

Returns:

true iff z is the sought-after real zero

solveAll

@Deprecated
public Complex[] solveAll(double[] coefficients,
                          double initial)
                   throws ConvergenceException,
                          FunctionEvaluationException

Deprecated.

in 2.2.

Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.

Parameters:

coefficients - the polynomial coefficients array

initial - the start value to use

Returns:

the point at which the function value 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

java.lang.IllegalArgumentException - if any parameters are invalid

solveAll

@Deprecated
public Complex[] solveAll(Complex[] coefficients,
                          Complex initial)
                   throws MaxIterationsExceededException,
                          FunctionEvaluationException

Deprecated.

in 2.2.

Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.

Parameters:

coefficients - the polynomial coefficients array

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

@Deprecated
public Complex solve(Complex[] coefficients,
                     Complex initial)
              throws MaxIterationsExceededException,
                     FunctionEvaluationException

Deprecated.

in 2.2.

Find a complex root for the polynomial with the given coefficients, starting from the given initial value.

Parameters:

coefficients - the polynomial coefficients array

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