jdistlib.math.opt

Class Optimization

java.lang.Object

jdistlib.math.opt.Optimization

public class Optimization
extends java.lang.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

Modifier and Type	Method and Description
static void	main(java.lang.String[] args)
static double	optimize(UnivariateFunction f, double ax, double bx) Brent's minimization function with default tolerance (1e-10)
static 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 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

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

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(java.lang.String[] args)