Class 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) $
    • 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