Package 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

  • Constructor Details

    • 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 Details

    • 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 full set of complex roots of the polynomial
      Throws:
      TooManyEvaluationsException - if the maximum number of evaluations is exceeded when solving for one of the roots
      NullArgumentException - if the coefficients is null.
      NoDataException - if the coefficients array is empty.
      Since:
      3.1

    • solveAllComplex

      public Complex[] solveAllComplex(double[] coefficients, double initial, int maxEval) 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
      maxEval - maximum number of evaluations
      Returns:
      the full set of complex roots of the polynomial
      Throws:
      TooManyEvaluationsException - if the maximum number of evaluations is exceeded when solving for one of the roots
      NullArgumentException - if the coefficients is null
      NoDataException - if the coefficients array is empty
      Since:
      3.5

    • 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:
      a complex root of the polynomial
      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, int maxEval) 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
      maxEval - maximum number of evaluations
      Returns:
      a complex root of the polynomial
      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