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) $
  • Constructor Details

  • Method Details

    • 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
      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
      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
      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
      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
      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
      IllegalArgumentException - if any parameters are invalid
    • solve

      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
      IllegalArgumentException - if any parameters are invalid