QuasiRandom
Class LowDiscrepancySequence

java.lang.Object
  extended byQuasiRandom.LowDiscrepancySequence
Direct Known Subclasses:
DigitalRandomSequence, Halton, NX, Sobol, Uniform

public abstract class LowDiscrepancySequence
extends java.lang.Object

Interface and methods to compute L2-discrepancy for low discrepancy sequences.


Constructor Summary
LowDiscrepancySequence(int dim)
           
 
Method Summary
abstract  java.lang.String getName()
          Name of sequence.
 double L2_discrepancy(int N, double[][] r)
          The L^2-discrepancy of the first N points.
 double L2_discrepancy(int N, double[][] r, double x)
          The L^2-discrepancy of the first N points.
abstract  double[] nextPoint()
          Returns the next point in the sequence.
 void nextPoint(double[] r)
          Writes the next point of the sequence into the array r.
 double[] nextQuasiNormalVector()
          The transform of the next uniform point in the sequence to a quasinormal vector.
 ProjectionPlot2D projectionPlot(int i, int j, int nPoints)
          JFrame capable of drawing the projections of the sequence on any pair of dimensions (i,j) (axes parallel two dimensional plane).
 void restart()
          POINT GENERATION
 
Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait
 

Constructor Detail

LowDiscrepancySequence

public LowDiscrepancySequence(int dim)
Parameters:
dim - dimension
Method Detail

getName

public abstract java.lang.String getName()
Name of sequence.


restart

public void restart()
POINT GENERATION


nextPoint

public abstract double[] nextPoint()
Returns the next point in the sequence.


nextPoint

public void nextPoint(double[] r)

Writes the next point of the sequence into the array r. Useful when discrepancy is computed.


L2_discrepancy

public double L2_discrepancy(int N,
                             double[][] r)

The L^2-discrepancy of the first N points. This computes the L^2 discrepancy T_N of the first N points r[j][], j=0,...,N-1.

Parameters:
N - number of points.
r - array of points r[j][], j=0,...,N-1.

L2_discrepancy

public double L2_discrepancy(int N,
                             double[][] r,
                             double x)

The L^2-discrepancy of the first N points. This computes the L^2 discrepancy T_{N+1} of the first N+1 points r[j][], j=0,...,N from the discrepancy x=T_N of the first N points based on the recursion followed by the quantities h_N=(NT_N)^2/2.

Use this method if the L2-discrepancy is to be computed for all n=1,2,3,... (number of points).

Parameters:
N - number of points.
r - array of points r[j][], j=0,...,N.
x - discrepancy T_N.

nextQuasiNormalVector

public double[] nextQuasiNormalVector()
The transform of the next uniform point in the sequence to a quasinormal vector. Method of transform: coordinatewise inverse normal CDF.


projectionPlot

public ProjectionPlot2D projectionPlot(int i,
                                       int j,
                                       int nPoints)

JFrame capable of drawing the projections of the sequence on any pair of dimensions (i,j) (axes parallel two dimensional plane).

Parameters:
i - dimension.
j - dimension.
nPoints - number of points to be plotted.