fr.cnes.sirius.patrius.math.analysis.solver

Class LaguerreSolver

java.lang.Object

fr.cnes.sirius.patrius.math.analysis.solver.BaseAbstractUnivariateSolver<PolynomialFunction>

fr.cnes.sirius.patrius.math.analysis.solver.AbstractPolynomialSolver

fr.cnes.sirius.patrius.math.analysis.solver.LaguerreSolver

All Implemented Interfaces:

BaseUnivariateSolver<PolynomialFunction>, PolynomialSolver, Serializable

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 18108 2017-10-04 06:45:27Z bignon $

See Also:

Serialized Form

Constructor Summary

Constructors

Constructor and 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

Modifier and Type	Method and Description
double	doSolve() Method for implementing actual optimization algorithms in derived classes.
Complex[]	solveAllComplex(double[] coefficients, double initial) Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
Complex[]	solveAllComplex(double[] coefficients, double[] initials, int[] maxEvals) Find all complex roots for the polynomial with the given coefficients, starting from the given initial value.
Complex[]	solveAllComplex(double[] coefficients, double initial, int maxEval) 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.
Complex	solveComplex(double[] coefficients, double[] initials, int[] maxEvals) Find a complex root for the polynomial with the given coefficients, starting from the given initial value.
Complex	solveComplex(double[] coefficients, double initial, int maxEval) Find a complex root for the polynomial with the given coefficients, starting from the given initial value.

Methods inherited from class fr.cnes.sirius.patrius.math.analysis.solver.AbstractPolynomialSolver

getCoefficients, setup

Methods inherited from class fr.cnes.sirius.patrius.math.analysis.solver.BaseAbstractUnivariateSolver

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

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface fr.cnes.sirius.patrius.math.analysis.solver.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()

Method for implementing actual optimization algorithms in derived classes.

Specified by:

doSolve in class BaseAbstractUnivariateSolver<PolynomialFunction>

Returns:

the root.

solveAllComplex

public Complex[] solveAllComplex(double[] coefficients,
                                 double initial)

Find all complex roots for the polynomial with the given coefficients, starting from the given initial value. A default value is used for the maximum number of iterations
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

TooManyEvaluationsException - if too many evaluations are required

Since:

3.1

solveAllComplex

public Complex[] solveAllComplex(double[] coefficients,
                                 double initial,
                                 int maxEval)

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.

maxEval - maximum number of iterations

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

TooManyEvaluationsException - if too many evaluations are required

Since:

4.17

solveAllComplex

public Complex[] solveAllComplex(double[] coefficients,
                                 double[] initials,
                                 int[] maxEvals)

Find all complex roots for the polynomial with the given coefficients, starting from the given initial value. Multiple initial values and multiple maximum number of iterations for each initial value can be given as input.
Note: This method is not part of the API of BaseUnivariateSolver.

Parameters:

coefficients - Polynomial coefficients

initials - Array of possible start values

maxEvals - Array of maximum number of iterations for each start value

Returns:

the point at which the function value is zero

Throws:

DimensionMismatchException - if the start values array and the maximum number of iterations array aren't the same length

TooManyEvaluationsException - if the maximum number of evaluations is exceeded

NullArgumentException - if the coefficients is null

NoDataException - if the coefficients array is empty

TooManyEvaluationsException - if too many evaluations are required

Since:

4.17

solveComplex

public Complex solveComplex(double[] coefficients,
                            double initial)

Find a complex root for the polynomial with the given coefficients, starting from the given initial value.
A default value of maximum number of iterations is used. 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:

NullArgumentException - if the coefficients is null

NoDataException - if the coefficients array is empty

TooManyEvaluationsException - if too many evaluations are required

Since:

3.1

solveComplex

public Complex solveComplex(double[] coefficients,
                            double initial,
                            int maxEval)

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.

maxEval - Maximum number of iterations

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

TooManyEvaluationsException - if too many evaluations are required

Since:

4.17

solveComplex

public Complex solveComplex(double[] coefficients,
                            double[] initials,
                            int[] maxEvals)

Find a complex root for the polynomial with the given coefficients, starting from the given initial value.
Multiple initial values and multiple maximum number of iterations for each initial value can be given as input. Note: This method is not part of the API of BaseUnivariateSolver.

Parameters:

coefficients - Polynomial coefficients

initials - Array of possible start values.

maxEvals - Array of maximum number of iterations for each start value

Returns:

the point at which the function value is zero

Throws:

DimensionMismatchException - if the start values array and the maximum number of iterations array aren't the same length

TooManyEvaluationsException - if the maximum number of evaluations is exceeded

NullArgumentException - if the coefficients is null

NoDataException - if the coefficients array is empty

TooManyEvaluationsException - if too many evaluations are required

Since:

4.17