Class BrentSolver

  • All Implemented Interfaces:
    BaseUnivariateSolver<UnivariateFunction>, UnivariateSolver

    public class BrentSolver
    extends AbstractUnivariateSolver
    This class implements the Brent algorithm for finding zeros of real univariate functions. The function should be continuous but not necessarily smooth. The solve method returns a zero x of the function f in the given interval [a, b] to within a tolerance 2 eps abs(x) + t where eps is the relative accuracy and t is the absolute accuracy.

    The given interval must bracket the root.

    The reference implementation is given in chapter 4 of

    Algorithms for Minimization Without Derivatives, Richard P. Brent, Dover, 2002
    See Also:
    BaseAbstractUnivariateSolver
    • Field Detail

      • DEFAULT_ABSOLUTE_ACCURACY

        private static final double DEFAULT_ABSOLUTE_ACCURACY
        Default absolute accuracy.
        See Also:
        Constant Field Values
    • Constructor Detail

      • BrentSolver

        public BrentSolver()
        Construct a solver with default absolute accuracy (1e-6).
      • BrentSolver

        public BrentSolver​(double absoluteAccuracy)
        Construct a solver.
        Parameters:
        absoluteAccuracy - Absolute accuracy.
      • BrentSolver

        public BrentSolver​(double relativeAccuracy,
                           double absoluteAccuracy)
        Construct a solver.
        Parameters:
        relativeAccuracy - Relative accuracy.
        absoluteAccuracy - Absolute accuracy.
      • BrentSolver

        public BrentSolver​(double relativeAccuracy,
                           double absoluteAccuracy,
                           double functionValueAccuracy)
        Construct a solver.
        Parameters:
        relativeAccuracy - Relative accuracy.
        absoluteAccuracy - Absolute accuracy.
        functionValueAccuracy - Function value accuracy.
        See Also:
        BaseAbstractUnivariateSolver(double,double,double)
    • Method Detail

      • brent

        private double brent​(double lo,
                             double hi,
                             double fLo,
                             double fHi)
        Search for a zero inside the provided interval. This implementation is based on the algorithm described at page 58 of the book
        Algorithms for Minimization Without Derivatives, Richard P. Brent, Dover 0-486-41998-3
        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 value where the function is zero.