QuasiRandom
Class Intgrnd

java.lang.Object
  QuasiRandom.CubeFunction
      QuasiRandom.SeparableCubeFunction
          QuasiRandom.Intgrnd

Direct Known Subclasses:

Intgrnd_1, Intgrnd_2, Intgrnd_3, Intgrnd_4, Intgrnd_5, Intgrnd_6

public abstract class Intgrnd

extends SeparableCubeFunction

Function f(x)=h(x_1)*h(x_2)*...*h(x_d), where d=dimension, h(u)=g(m*u-[m*u]) and g=g(u) is a function of one variable u\in(0,1) and [t] denotes the largest integer not greater than t as usual.

Note that the function h is periodic with m periods on (0,1) since it repeats the behaviour of g on each interval [j/m,(j+1)/m] and so in particular integral_0^1 h(t)dt = integral_0^1 g(u)du.

If the function g has one peak on (0,1) then h has m peaks on (0,1) and f will have m^dim peaks on the unit cube Q.

Constructor Summary

Intgrnd(int dim, int m)

Method Summary

abstract double	g(double u) The function defining the factor h as h(u)=g(m*u-[m*u]).
abstract double	gIntegral() The integral of g over (0,1).
double	h(double u) h IN TERMS OF g
double	hIntegral() The integral of h over (0,1).

Methods inherited from class QuasiRandom.SeparableCubeFunction

integral, value

Methods inherited from class QuasiRandom.CubeFunction

getName

Methods inherited from class java.lang.Object

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

Constructor Detail

Intgrnd

public Intgrnd(int dim,
               int m)

Parameters:

dim - dimension

m - number of periods of factor h on (0,1).

Method Detail

g

public abstract double g(double u)

The function defining the factor h as h(u)=g(m*u-[m*u]).

gIntegral

public abstract double gIntegral()

The integral of g over (0,1).

h

public double h(double u)

h IN TERMS OF g

Specified by:

h in class SeparableCubeFunction

Parameters:

u - independent one dimensional variable.

hIntegral

public double hIntegral()

The integral of h over (0,1).

Specified by:

hIntegral in class SeparableCubeFunction