## Class 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
• ### Constructor Summary

Constructors
Constructor Description
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

All Methods
Modifier and Type Method Description
double doSolve()
Method for implementing actual optimization algorithms in derived classes.
org.apache.commons.numbers.complex.Complex[] solveAllComplex​(double[] coefficients, double initial)
Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
org.apache.commons.numbers.complex.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.math4.legacy.analysis.solvers.AbstractPolynomialSolver

getCoefficients, setup
• ### Methods inherited from class org.apache.commons.math4.legacy.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.math4.legacy.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
• #### solveAllComplex

public org.apache.commons.numbers.complex.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 org.apache.commons.numbers.complex.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