SSJ  3.3.1
Stochastic Simulation in Java
Public Member Functions | List of all members
DiscL2Symmetric Class Reference

COMPLÉTER LA DOC ICI. More...

Inheritance diagram for DiscL2Symmetric:
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Collaboration diagram for DiscL2Symmetric:
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Public Member Functions

double compute (double[][] points, int n, int s, double[] gamma)
 
 DiscL2Symmetric (double[][] points, int n, int s)
 Constructor with the \(n\) points points[i] in \(s\) dimensions. More...
 
 DiscL2Symmetric (int n, int s)
 Constructor with \(n\) points in dimension \(s\). More...
 
 DiscL2Symmetric (PointSet set)
 Constructor with the point set set. More...
 
 DiscL2Symmetric ()
 Empty constructor. More...
 
double compute (double[][] points, int n, int s)
 Computes the \(\mathcal{L}_2\)-symmetric discrepancy for the set of \(n\) \(s\)-dimensional points points, using formula ( sym ).
 
double compute (double[] T, int n)
 Computes the \(\mathcal{L}_2\)-symmetric discrepancy for the set of \(n\) 1-dimensional points \(T\), using formula ( symD1 ).
 
- Public Member Functions inherited from Discrepancy
 Discrepancy (double[][] points, int n, int s)
 Constructor with the \(n\) points points[i] in \(s\) dimensions. More...
 
 Discrepancy (double[][] points, int n, int s, double[] gamma)
 Constructor with the \(n\) points points[i] in \(s\) dimensions and the \(s\) weight factors gamma[ \(j\)], \(j = 0, 1, …, (s-1)\). More...
 
 Discrepancy (int n, int s, double[] gamma)
 The number of points is \(n\), the dimension \(s\), and the \(s\) weight factors are gamma[ \(j\)], \(j = 0, 1, …, (s-1)\). More...
 
 Discrepancy (PointSet set)
 Constructor with the point set set. More...
 
 Discrepancy ()
 Empty constructor. More...
 
double compute ()
 Computes the discrepancy of all the points in maximal dimension (dimension of the points).
 
double compute (int s)
 Computes the discrepancy of all the points in dimension \(s\).
 
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.
 
abstract double compute (double[][] points, int n, int s)
 Computes the discrepancy of the first n points of points in dimension s with weights \(=1\).
 
double compute (double[][] points)
 Computes the discrepancy of all the points of points in maximum dimension. More...
 
double compute (double[] T, int n)
 Computes the discrepancy of the first n points of T in 1 dimension. More...
 
double compute (double[] T)
 Computes the discrepancy of all the points of T in 1 dimension. More...
 
double compute (double[] T, int n, double gamma)
 Computes the discrepancy of the first n points of T in 1 dimension with weight gamma.
 
double compute (PointSet set, double[] gamma)
 Computes the discrepancy of all the points in set in the same dimension as the point set and with weights gamma.
 
double compute (PointSet set)
 Computes the discrepancy of all the points in set in the same dimension as the point set. More...
 
int getNumPoints ()
 Returns the number of points \(n\).
 
int getDimension ()
 Returns the dimension of the points \(s\).
 
void setPoints (double[][] points, int n, int s)
 Sets the points to points and the dimension to \(s\). More...
 
void setPoints (double[][] points)
 Sets the points to points. More...
 
void setGamma (double[] gam, int s)
 Sets the weight factors to gam for each dimension up to \(s\).
 
double [] getGamma ()
 Returns the weight factors gamma for each dimension up to \(s\).
 
String toString ()
 Returns the parameters of this class.
 
String formatPoints ()
 Returns all the points of this class.
 
String getName ()
 Returns the name of the Discrepancy.
 

Additional Inherited Members

- Static Public Member Functions inherited from Discrepancy
static double [][] toArray (PointSet set)
 Returns all the \(n\) points ( \(s\)-dimensional) of umontreal.ssj.hups.PointSet set as an array points[ \(n\)][ \(s\)].
 
static DoubleArrayList sort (double[] T, int n)
 Sorts the first \(n\) points of \(T\). More...
 
- Protected Member Functions inherited from Discrepancy
void appendGamma (StringBuffer sb, double[] gamma, int s)
 
- Static Protected Member Functions inherited from Discrepancy
static void setONES (int s)
 
- Protected Attributes inherited from Discrepancy
double [] gamma
 
double [][] Points
 
int dim
 
int numPoints
 
- Static Protected Attributes inherited from Discrepancy
static double [] ONES = { 1 }
 
- Static Package Attributes inherited from Discrepancy
static final double UNSIX = 1.0/6.0
 
static final double QUARAN = 1.0/42.0
 
static final double UNTRENTE = 1.0 / 30.0
 
static final double DTIERS = 2.0 / 3.0
 
static final double STIERS = 7.0 / 3.0
 
static final double QTIERS = 14.0 / 3.0
 

Detailed Description

COMPLÉTER LA DOC ICI.

This class computes the \(\mathcal{L}_2\)-symmetric discrepancy for a set of points [81], [167] , given by

\[ [\mathcal{D}_s(\mathcal{P})]^2 = \left(\frac{4}{3}\right)^s - \frac{2}{n} \sum_{i=1}^n \prod_{k=1}^s \left(1 + 2z_{ik} - 2z_{ik}^2\right) + \frac{2^s}{n^2} \sum_{i=1}^n\sum_{j=1}^n \prod_{k=1}^s \left(1 - |z_{ik} - z_{jk}|\right), \tag{sym} \]

where \(n\) is the number of points of \(\mathcal{P}\), \(s\) is the dimension, and \(z_{ik}\) is the \(k\)-th coordinate of point \(i\).

In one dimension, formula ( sym ) is equivalent to

\[ [\mathcal{D}_s(\mathcal{P})]^2 = \frac{4}{3} - \frac{4}{n} \sum_{i=1}^n z_i(1 - z_i) - \frac{2}{n^2} \sum_{i=1}^n\sum_{j=1}^n|z_i - z_j|, \tag{symD1} \]

where \(z_i\) is the coordinate of point \(i\).

Constructor & Destructor Documentation

◆ DiscL2Symmetric() [1/4]

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() [2/4]

DiscL2Symmetric ( int  n,
int  s 
)

Constructor with \(n\) points in dimension \(s\).

The \(n\) points will be chosen later.

◆ DiscL2Symmetric() [3/4]

Constructor with the point set set.

All the points are copied in an internal array.

◆ DiscL2Symmetric() [4/4]

Empty constructor.

One must set the points and the dimension before calling any method.


The documentation for this class was generated from the following file: