SSJ
V. labo.

umontreal.iro.lecuyer.discrepancy
Class DiscL2Symmetric

java.lang.Object
  extended by umontreal.iro.lecuyer.discrepancy.Discrepancy
      extended by umontreal.iro.lecuyer.discrepancy.DiscL2Symmetric

public class DiscL2Symmetric
extends Discrepancy

COMPLÉTER LA DOC ICI.

This class computes the L2-symmetric discrepancy for a set of points, given by

[Ds(P)]2 = ($\displaystyle {\textstyle\frac{4}{3}}$)s - $\displaystyle {\frac{2}{n}}$i=1nk=1s(1 + 2zik -2zik2) + $\displaystyle {\frac{{2^s}}{{n^2}}}$i=1nj=1nk=1s(1 - | zik - zjk|),

where n is the number of points of P, s is the dimension, and zik is the k-th coordinate of point i.

In one dimension, formula is equivalent to

[Ds(P)]2 = [tex2html_wrap_indisplay205] - $\displaystyle {\frac{4}{n}}$i=1nzi(1 - zi) - $\displaystyle {\frac{{2}}{{n^2}}}$i=1nj=1n| zi - zj|,

where zi is the coordinate of point i.


Constructor Summary
DiscL2Symmetric()
          Empty constructor.
DiscL2Symmetric(double[][] points, int n, int s)
          Constructor with the n points points[i] in s dimensions.
DiscL2Symmetric(int n, int s)
          Constructor with n points in dimension s.
DiscL2Symmetric(PointSet set)
          Constructor with the point set set.
 
Method Summary
 double compute(double[][] points, int n, int s)
          Computes the L2-symmetric discrepancy for the set of n s-dimensional points points, using formula.
 double compute(double[][] points, int n, int s, double[] gamma)
          Computes the discrepancy of the first n points of points in dimension s with weights gamma.
 double compute(double[] T, int n)
          Computes the L2-symmetric discrepancy for the set of n 1-dimensional points T, using formula.
 
Methods inherited from class umontreal.iro.lecuyer.discrepancy.Discrepancy
compute, compute, compute, compute, compute, compute, compute, formatPoints, getDimension, getGamma, getName, getNumPoints, setGamma, setPoints, setPoints, sort, toArray, toString
 
Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, wait, wait, wait
 

Constructor Detail

DiscL2Symmetric

public DiscL2Symmetric(double[][] points,
                       int n,
                       int s)
Constructor with the n points points[i] in s dimensions. points[i][j] is the j-th coordinate of point i. Both i and j start at 0.


DiscL2Symmetric

public DiscL2Symmetric(int n,
                       int s)
Constructor with n points in dimension s. The n points will be chosen later.


DiscL2Symmetric

public DiscL2Symmetric(PointSet set)
Constructor with the point set set. All the points are copied in an internal array.


DiscL2Symmetric

public DiscL2Symmetric()
Empty constructor. One must set the points and the dimension before calling any method.

Method Detail

compute

public double compute(double[][] points,
                      int n,
                      int s,
                      double[] gamma)
Description copied from class: Discrepancy
Computes the discrepancy of the first n points of points in dimension s with weights gamma.

Overrides:
compute in class Discrepancy

compute

public double compute(double[][] points,
                      int n,
                      int s)
Computes the L2-symmetric discrepancy for the set of n s-dimensional points points, using formula.

Specified by:
compute in class Discrepancy

compute

public double compute(double[] T,
                      int n)
Computes the L2-symmetric discrepancy for the set of n 1-dimensional points T, using formula.

Overrides:
compute in class Discrepancy

SSJ
V. labo.

To submit a bug or ask questions, send an e-mail to Pierre L'Ecuyer.