edu.rit.numeric

Class MDMinimizationDownhillSimplex

java.lang.Object

edu.rit.numeric.MDMinimizationDownhillSimplex

public class MDMinimizationDownhillSimplex
extends java.lang.Object

Class MDMinimizationDownhillSimplex finds a minimum of a multidimensional function using the downhill simplex method of Nelder and Mead. The function has N inputs and is represented by an object that implements interface MDFunction. The minimize() method finds a (local) minimum in the function. The input to the minimize() method is an N-dimensional simplex, namely a group of N+1 points in N dimensions, each point different from all the others. Typically, one point of the simplex is an initial guess for the solution, and the other points of the simplex are perturbations of the initial guess. The minimize() method evaluates the function at each point of the simplex and moves the simplex through N-dimensional space to minimize the smallest function value of any point in the simplex, stopping when the relative difference between the smallest and largest function values of any points in the simplex falls below a tolerance. The output from the minimize() method is the final simplex, with the smallest-function-value point at position 0. The inputs to and outputs from the minimize() method are stored in the fields of an instance of class MDMinimizationDownhillSimplex.

Field Summary

Fields

Modifier and Type	Field and Description
boolean	debug Debug flag.
double[]	f Function values of the simplex points.
MDFunction	fcn The multidimensional function to be minimized.
int	N The number of function arguments.
double	tol Tolerance.
double[][]	x The simplex.

Constructor Summary

Constructors

Constructor and Description
MDMinimizationDownhillSimplex(MDFunction theFunction) Construct a new multidimensional minimization object for the given function.

Method Summary

Modifier and Type	Method and Description
void	minimize() Minimize the multidimensional function.
void	setSimplex(double[] x, double delta) Set the simplex to the given point plus the same perturbation along each dimension.
void	setSimplex(double[] x, double[] delta) Set the simplex to the given point plus a different perturbation along each dimension.

Methods inherited from class java.lang.Object

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

Field Detail

fcn

public final MDFunction fcn

The multidimensional function to be minimized.

N

public final int N

The number of function arguments.

x

public final double[][] x

The simplex. This is an N+1-element array of N-element points. On input to the minimize() method, x contains a simplex with an initial estimate of the solution. On output from the minimize() method, x contains the final simplex, and x[0] contains the solution, namely the simplex point with the smallest function value.

f

public final double[] f

Function values of the simplex points. An N+1-element array. On output from the minimize() method, f[i] contains the function value for simplex point x[i], 0 ≤ i ≤ N−1. In particular, f[0] contains the minimized function value for the solution.

tol

public double tol

Tolerance. An input to the minimize() method. Must be > 0. Termination occurs when the relative difference between the smallest and largest function values of points in the simplex is less than the tolerance. The default tolerance is 1×10⁻⁶.

debug

public boolean debug

Debug flag. An input to the minimize() method. If true, the subclassDebug() method is called at the beginning of every iteration. The default setting is false.

Constructor Detail

MDMinimizationDownhillSimplex

public MDMinimizationDownhillSimplex(MDFunction theFunction)

Construct a new multidimensional minimization object for the given function. Field fcn is set to theFunction. Field N is set by calling the function's argumentLength() method. Field x, the simplex, is allocated with the proper size; all simplex points are initially 0. Field f, the function values, is allocated with the proper size.

Parameters:

theFunction - Multidimensional function to be minimized.

Throws:

java.lang.NullPointerException - (unchecked exception) Thrown if theFunction is null.

Method Detail

setSimplex

public void setSimplex(double[] x,
                       double delta)

Set the simplex to the given point plus the same perturbation along each dimension. The field x[0] is set to x; the field x[1] is set to x with delta added to element 0; the field x[2] is set to x with delta added to element 1; and so on.

Parameters:

x - Simplex point. Must be an N-element array.

delta - Perturbation along every dimension. Must be nonzero.

setSimplex

public void setSimplex(double[] x,
                       double[] delta)

Set the simplex to the given point plus a different perturbation along each dimension. The field x[0] is set to x; the field x[1] is set to x with delta[0] added to element 0; the field x[2] is set to x with delta[1] added to element 1; and so on.

Parameters:

x - Simplex point. Must be an N-element array.

delta - Perturbations along each dimension. All must be nonzero.

minimize

public void minimize()

Minimize the multidimensional function. On input, the field x must be filled in with an initial simplex, and the field tol must be set to the desired tolerance. On output, the field x contains the solution. For further information, see the documentation for each field.

Throws:

java.lang.IllegalArgumentException - (unchecked exception) Thrown if tol ≤ 0.

TooManyIterationsException - (unchecked exception) Thrown if too many function evaluations (5,000) occurred without finding a minimum.