## 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