org.apache.commons.math3.analysis.solvers
Class LaguerreSolver

java.lang.Object
  org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver<PolynomialFunction>
      org.apache.commons.math3.analysis.solvers.AbstractPolynomialSolver
          org.apache.commons.math3.analysis.solvers.LaguerreSolver

All Implemented Interfaces:

BaseUnivariateSolver<PolynomialFunction>, PolynomialSolver

public class LaguerreSolver
extends AbstractPolynomialSolver

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. The algorithm requires a bracketing condition.

Since:

1.2

Version:

$Id: LaguerreSolver.java 7721 2013-02-14 14:07:13Z CardosoP $

Constructor Summary

LaguerreSolver()
Construct a solver with default accuracy (1e-6).

LaguerreSolver(double absoluteAccuracy)
Construct a solver.

LaguerreSolver(double relativeAccuracy, double absoluteAccuracy)
Construct a solver.

LaguerreSolver(double relativeAccuracy, double absoluteAccuracy, double functionValueAccuracy)
Construct a solver.

Method Summary

double	doSolve() Method for implementing actual optimization algorithms in derived classes.
double	laguerre(double lo, double hi, double fLo, double fHi) Deprecated. This method should not be part of the public API: It will be made private in version 4.0.
Complex[]	solveAllComplex(double[] coefficients, double initial) Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
Complex	solveComplex(double[] coefficients, double initial) Find a complex root for the polynomial with the given coefficients, starting from the given initial value.

Methods inherited from class org.apache.commons.math3.analysis.solvers.AbstractPolynomialSolver

getCoefficients, setup

Methods inherited from class org.apache.commons.math3.analysis.solvers.BaseAbstractUnivariateSolver

computeObjectiveValue, getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMax, getMaxEvaluations, getMin, getRelativeAccuracy, getStartValue, incrementEvaluationCount, isBracketing, isSequence, solve, solve, solve, verifyBracketing, verifyInterval, verifySequence

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.math3.analysis.solvers.BaseUnivariateSolver

getAbsoluteAccuracy, getEvaluations, getFunctionValueAccuracy, getMaxEvaluations, getRelativeAccuracy, solve, solve, solve

Constructor Detail

LaguerreSolver

public LaguerreSolver()

Construct a solver with default accuracy (1e-6).

LaguerreSolver

public LaguerreSolver(double absoluteAccuracy)

Construct a solver.

Parameters:

absoluteAccuracy - Absolute accuracy.

LaguerreSolver

public LaguerreSolver(double relativeAccuracy,
                      double absoluteAccuracy)

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

LaguerreSolver

public LaguerreSolver(double relativeAccuracy,
                      double absoluteAccuracy,
                      double functionValueAccuracy)

Construct a solver.

Parameters:

relativeAccuracy - Relative accuracy.

absoluteAccuracy - Absolute accuracy.

functionValueAccuracy - Function value accuracy.

Method Detail

doSolve

public double doSolve()
               throws TooManyEvaluationsException,
                      NumberIsTooLargeException,
                      NoBracketingException

Method for implementing actual optimization algorithms in derived classes.

Specified by:

doSolve in class BaseAbstractUnivariateSolver<PolynomialFunction>

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

laguerre

@Deprecated
public double laguerre(double lo,
                                  double hi,
                                  double fLo,
                                  double fHi)

Deprecated. This method should not be part of the public API: It will be made private in version 4.0.

Find a real root in the given interval. Despite the bracketing condition, the root returned by LaguerreSolver.ComplexSolver.solve(Complex[],Complex) may not be a real zero inside [min, max]. For example, p(x) = x3 + 1, with min = -2, max = 2, initial = 0. When it occurs, this code calls LaguerreSolver.ComplexSolver.solveAll(Complex[],Complex) in order to obtain all roots and picks up one real root.

Parameters:

lo - Lower bound of the search interval.

hi - Higher bound of the search interval.

fLo - Function value at the lower bound of the search interval.

fHi - Function value at the higher bound of the search interval.

Returns:

the point at which the function value is zero.

solveAllComplex

public Complex[] solveAllComplex(double[] coefficients,
                                 double initial)
                          throws NullArgumentException,
                                 NoDataException,
                                 TooManyEvaluationsException

Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
Note: This method is not part of the API of BaseUnivariateSolver.

Parameters:

coefficients - Polynomial coefficients.

initial - Start value.

Returns:

the point at which the function value is zero.

Throws:

TooManyEvaluationsException - if the maximum number of evaluations is exceeded.

NullArgumentException - if the coefficients is null.

NoDataException - if the coefficients array is empty.

Since:

3.1

solveComplex

public Complex solveComplex(double[] coefficients,
                            double initial)
                     throws NullArgumentException,
                            NoDataException,
                            TooManyEvaluationsException

Find a complex root for the polynomial with the given coefficients, starting from the given initial value.
Note: This method is not part of the API of BaseUnivariateSolver.

Parameters:

coefficients - Polynomial coefficients.

initial - Start value.

Returns:

the point at which the function value is zero.

Throws:

TooManyEvaluationsException - if the maximum number of evaluations is exceeded.

NullArgumentException - if the coefficients is null.

NoDataException - if the coefficients array is empty.

Since:

3.1