Optimization
jdistlib.math

Class Optimization



  • public class Optimizationextends Object
    Function optimization routines. Currently only Brent's minimization routine. Maybe I'll add Nelder-Meade or other fancier methods.
    • Constructor Summary

      Constructors 
      Constructor and Description
      Optimization() 
    • Method Summary

      Methods 
      Modifier and TypeMethod and Description
      static voidmain(String[] args) 
      static doubleoptimize(UnivariateFunction f, double ax, double bx)
      Brent's minimization function with default tolerance (1e-10)
      static doubleoptimize(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 doublezeroin(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.
    • Constructor Detail

      • Optimization

        public Optimization()
    • Method Detail

      • 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)

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