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:
  • Field Details

    • DEFAULT_ABSOLUTE_ACCURACY

      private static final double DEFAULT_ABSOLUTE_ACCURACY
      Default absolute accuracy.
      See Also:
  • Constructor Details

    • 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:
  • Method Details

    • doSolve

      Method for implementing actual optimization algorithms in derived classes.
      Specified by:
      doSolve in class BaseAbstractUnivariateSolver<UnivariateFunction>
      Returns:
      the root.
      Throws:
      NoBracketingException - if the initial search interval does not bracket a root and the solver requires it.
      TooManyEvaluationsException - if the maximal number of evaluations is exceeded.
      NumberIsTooLargeException
    • 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.