keel.Algorithms.Preprocess.Missing_Values.EM.util

Class UnivariateMinimum

java.lang.Object

keel.Algorithms.Preprocess.Missing_Values.EM.util.UnivariateMinimum

public class UnivariateMinimum
extends java.lang.Object

minimization of a real-valued function of one variable without using derivatives.

algorithm: Brent's golden section method (Richard P. Brent. 1973. Algorithms for finding zeros and extrema of functions without calculating derivatives. Prentice-Hall.)

Version:

$Id: UnivariateMinimum.java,v 1.1 2010-07-03 22:51:08 keel Exp $

Author:

Korbinian Strimmer

Field Summary

Fields

Modifier and Type	Field and Description
double	f2minx curvature at minimum
double	fminx function value at minimum
int	maxFun maximum number of function evaluations (default 0 indicates no limit on calls)
double	minx last minimum
int	numFun total number of function evaluations neccessary

Constructor Summary

Constructors

Constructor and Description
UnivariateMinimum()

Method Summary

Modifier and Type	Method and Description
double	findMinimum(double x, UnivariateFunction f) Find minimum (first estimate given)
double	findMinimum(double x, UnivariateFunction f, int fracDigits) Find minimum (first estimate given, desired number of fractional digits specified)
double	findMinimum(UnivariateFunction f) Find minimum (no first estimate given)
double	findMinimum(UnivariateFunction f, int fracDigits) Find minimum (no first estimate given, desired number of fractional digits specified)
double	optimize(double x, UnivariateFunction f, double tol) The actual optimization routine (Brent's golden section method)
double	optimize(double x, UnivariateFunction f, double tol, double lowerBound, double upperBound) The actual optimization routine (Brent's golden section method)
double	optimize(UnivariateFunction f, double tol) The actual optimization routine (Brent's golden section method)
double	optimize(UnivariateFunction f, double tol, double lowerBound, double upperBound) The actual optimization routine (Brent's golden section method)

Methods inherited from class java.lang.Object

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

Field Detail

minx

public double minx

last minimum

fminx

public double fminx

function value at minimum

f2minx

public double f2minx

curvature at minimum

numFun

public int numFun

total number of function evaluations neccessary

maxFun

public int maxFun

maximum number of function evaluations (default 0 indicates no limit on calls)

Constructor Detail

UnivariateMinimum

public UnivariateMinimum()

Method Detail

findMinimum

public double findMinimum(double x,
                          UnivariateFunction f)

Find minimum (first estimate given)

Parameters:

x - first estimate

f - function

Returns:

position of minimum

findMinimum

public double findMinimum(double x,
                          UnivariateFunction f,
                          int fracDigits)

Find minimum (first estimate given, desired number of fractional digits specified)

Parameters:

x - first estimate

f - function

fracDigits - desired fractional digits

Returns:

position of minimum

findMinimum

public double findMinimum(UnivariateFunction f)

Find minimum (no first estimate given)

Parameters:

f - function

Returns:

position of minimum

findMinimum

public double findMinimum(UnivariateFunction f,
                          int fracDigits)

Find minimum (no first estimate given, desired number of fractional digits specified)

Parameters:

f - function

fracDigits - desired fractional digits

Returns:

position of minimum

optimize

public double optimize(UnivariateFunction f,
                       double tol,
                       double lowerBound,
                       double upperBound)

The actual optimization routine (Brent's golden section method)

Parameters:

f - univariate function

tol - absolute tolerance of each parameter

lowerBound - the lower bound of input

upperBound - the upper bound of input

Returns:

position of minimum

optimize

public double optimize(UnivariateFunction f,
                       double tol)

The actual optimization routine (Brent's golden section method)

Parameters:

f - univariate function

tol - absolute tolerance of each parameter

Returns:

position of minimum

optimize

public double optimize(double x,
                       UnivariateFunction f,
                       double tol,
                       double lowerBound,
                       double upperBound)

The actual optimization routine (Brent's golden section method)

Parameters:

x - initial guess

f - univariate function

tol - absolute tolerance of each parameter

lowerBound - the lower bound of input

upperBound - the upper bound of input

Returns:

position of minimum

optimize

public double optimize(double x,
                       UnivariateFunction f,
                       double tol)

The actual optimization routine (Brent's golden section method)

Parameters:

x - initial guess

f - univariate function

tol - absolute tolerance of each parameter bounded by the given bounds of the function f

Returns:

position of minimum