q1471341.mp1074.integration.lattice
Class Optimizer

java.lang.Object
  q1471341.mp1074.integration.lattice.Optimizer

public class Optimizer

extends java.lang.Object

This class optimizes generator vectors for lattice rules. Only generator vectors of Korobov form are tested for optimality.

Author:

Ulrich Telle

Constructor Summary

Optimizer()
Constructs a default Optimizer.

Optimizer(int alpha)
Constructs an Optimizer with specified value for alpha.

Optimizer(int nCopy, int alpha)
Constructs an Optimizer with specified value for nCopy> and alpha.

Method Summary

int[]	findOptimalZ(int s, int m) This method finds the appropriate generator vector z to minimize P_alpha(Qf)
int	getAlpha()
int	getNCopy()
void	setAlpha(int alpha)
void	setNCopy(int copy)

Methods inherited from class java.lang.Object

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

Constructor Detail

Optimizer

public Optimizer()

Constructs a default Optimizer. nCopy=1 and alpha=2

Optimizer

public Optimizer(int alpha)

Constructs an Optimizer with specified value for alpha. nCopy=1

Optimizer

public Optimizer(int nCopy,
                 int alpha)

Constructs an Optimizer with specified value for nCopy> and alpha. An instance of the lattice rule 'Method of good lattice points' is created for internal use in the optimization.

Method Detail

findOptimalZ

public int[] findOptimalZ(int s,
                          int m)

This method finds the appropriate generator vector z to minimize P_alpha(Qf)m, and a single generator vector z is chosen. The integrand is assumed to be periodic of period 1 in each argument, and is evaluated at each of the points x_i(1:s) = i * z(1:s) / m, for i = 0 to m-1. The integral is then approximated by the average of these values. Assuming that s and m are known, and that the integrand is not known beforehand, the accuracy of the method depends entirely on the choice of z. One method of choosing z is to search for the z among all candidates which minimizes a particular quantity P_alpha(Qf). Here only the vectors z of the form (1, L, L^2, ..., L^(S-1)), for L = 1 to M/2 are checked.

Parameters:

s - the spatial dimension.

m - the number of points to be used.

Returns:

z the optimal vector.

getAlpha

public int getAlpha()

Returns:

Returns the alpha value.

setAlpha

public void setAlpha(int alpha)

Parameters:

alpha - The alpha to set.

getNCopy

public int getNCopy()

Returns:

Returns the nCopy.

setNCopy

public void setNCopy(int copy)

Parameters:

copy - The nCopy to set.