Package jdistlib.math.opt

Class Optimization

java.lang.Object
jdistlib.math.opt.Optimization
public class Optimization extends Object
Function optimization routines. Currently only Brent's minimization routine. Maybe I'll add Nelder-Meade or other fancier methods.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Optimization()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    static void
    main(String[] args)
     
    static final double
    optimize(UnivariateFunction f, double ax, double bx)
    Brent's minimization function with default tolerance (1e-10)
    static final double
    optimize(UnivariateFunction f, double ax, double bx, double tol, int maxiter)
    Richard Brent's function minimization routine.
    Wikipedia's link
    Adapted from Netlib's fmin.
    Also looked at Numerical Methods in C, 2nd ed.
    static final double
    zeroin(UnivariateFunction f, double ax, double bx, double tol, int maxiter)
    ************************************************************************ C math library function ZEROIN - obtain a function zero within the given range Output Zeroin returns an estimate for the root with accuracy 4*EPSILON*abs(x) + tol Algorithm G.Forsythe, M.Malcolm, C.Moler, Computer methods for mathematical computations.

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Optimization

      public Optimization()

  • Method Details

    • optimize

      public static final double optimize(UnivariateFunction f, double ax, double bx)
      Brent's minimization function with default tolerance (1e-10)
      Parameters:
      f -
      ax -
      bx -
      Returns:
      the x at which f(x) is the minimum value

    • optimize

      public static final double optimize(UnivariateFunction f, double ax, double bx, double tol, int maxiter)
      Richard Brent's function minimization routine.
      Wikipedia's link
      Adapted from Netlib's fmin.
      Also looked at Numerical Methods in C, 2nd ed. Chapter 10 section 1 and 2.
      Parameters:
      f - the function to minimize
      ax - lower bound
      bx - upper bound
      tol - tolerance
      maxiter - the maximum number of iterations

    • zeroin

      public static final double zeroin(UnivariateFunction f, double ax, double bx, double tol, int maxiter)
      ************************************************************************
                            C math library
 function ZEROIN - obtain a function zero within the given range

 Output
        Zeroin returns an estimate for the root with accuracy
        4*EPSILON*abs(x) + tol

 Algorithm
        G.Forsythe, M.Malcolm, C.Moler, Computer methods for mathematical
        computations. M., Mir, 1980, p.180 of the Russian edition

        The function makes use of the bisection procedure combined with
        the linear or quadric inverse interpolation.
        At every step program operates on three abscissae - a, b, and c.
        b - the last and the best approximation to the root
        a - the last but one approximation
        c - the last but one or even earlier approximation than a that
                1) |f(b)| <= |f(c)|
                2) f(b) and f(c) have opposite signs, i.e., b and c confine
                   the root
        At every step Zeroin selects one of the two new approximations, the
        former being obtained by the bisection procedure and the latter
        resulting in the interpolation (if a,b, and c are all different
        the quadric interpolation is utilized, otherwise the linear one).
        If the latter (i.e. obtained by the interpolation) point is
        reasonable (i.e. lies within the current interval [b,c] not being
        too close to the boundaries) it is accepted. The bisection result
        is used in the other case. Therefore, the range of uncertainty is
        ensured to be reduced at least by the factor 1.6



 NOTE:  uniroot() --> do_zeroin2()  --- in  ../main/optimize.c
                                              ~~~~~~~~~~~~~~~~~~
      Parameters:
      f - The function whose zero is sought
      ax - Root will be sought for within a range [ax,bx]
      bx -
      tol - Acceptable tolerance for the root value. May be specified as 0.0 to cause the program to find the root as accurate as possible.
      maxiter - Max. iterations
      Returns:
      the x where f(x) == 0

    • main

      public static void main(String[] args)