COMPLÉTER LA DOC ICI. More...
Public Member Functions | |
| 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. | |
| 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. | |
| DiscL2Symmetric () | |
| Empty constructor. | |
| 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. | |
| Public Member Functions inherited from umontreal.ssj.discrepancy.Discrepancy | |
| Discrepancy (double[][] points, int n, int s) | |
| Constructor with the \(n\) points points[i] in \(s\) dimensions. | |
| 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[ \(j\)], \(j = 0, 1,
…, (s-1)\). | |
| Discrepancy (int n, int s, double[] gamma) | |
| The number of points is \(n\), the dimension \(s\), and the. | |
| Discrepancy (PointSet set) | |
| Constructor with the point set set. | |
| Discrepancy () | |
| Empty constructor. | |
| 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) |
| Computes the discrepancy of all the points of points in maximum dimension. | |
| double | compute (double[] T) |
| Computes the discrepancy of all the points of T in 1 dimension. | |
| 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. | |
| 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 \(s\). | |
| void | setPoints (double[][] points) |
| Sets the points to points. | |
| 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 umontreal.ssj.discrepancy.Discrepancy | |
| static double[][] | toArray (PointSet set) |
| Returns all the \(n\) points ( \(s\)-dimensional) of. | |
| static DoubleArrayList | sort (double[] T, int n) |
| Sorts the first \(n\) points of \(T\). | |
Detailed Description
COMPLÉTER LA DOC ICI.
This class computes the \(\mathcal{L}_2\)-symmetric discrepancy for a set of points [78],
[163] , 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 \(i\).
Definition at line 55 of file DiscL2Symmetric.java.
Constructor & Destructor Documentation
◆ DiscL2Symmetric() [1/4]
| umontreal.ssj.discrepancy.DiscL2Symmetric.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.
Definition at line 67 of file DiscL2Symmetric.java.
◆ DiscL2Symmetric() [2/4]
| umontreal.ssj.discrepancy.DiscL2Symmetric.DiscL2Symmetric | ( | int | n, |
| int | s ) |
Constructor with \(n\) points in dimension \(s\).
The \(n\) points will be chosen later.
Definition at line 75 of file DiscL2Symmetric.java.
◆ DiscL2Symmetric() [3/4]
| umontreal.ssj.discrepancy.DiscL2Symmetric.DiscL2Symmetric | ( | PointSet | set | ) |
Constructor with the point set set.
All the points are copied in an internal array.
Definition at line 83 of file DiscL2Symmetric.java.
◆ DiscL2Symmetric() [4/4]
| umontreal.ssj.discrepancy.DiscL2Symmetric.DiscL2Symmetric | ( | ) |
Empty constructor.
One must set the points and the dimension before calling any method.
Definition at line 91 of file DiscL2Symmetric.java.
Member Function Documentation
◆ compute() [1/3]
| double umontreal.ssj.discrepancy.DiscL2Symmetric.compute | ( | double[] | T, |
| int | n ) |
Computes the \(\mathcal{L}_2\)-symmetric discrepancy for the set of \(n\) 1-dimensional points.
\(T\), using formula ( symD1 ).
Reimplemented from umontreal.ssj.discrepancy.Discrepancy.
Definition at line 137 of file DiscL2Symmetric.java.
◆ compute() [2/3]
| double umontreal.ssj.discrepancy.DiscL2Symmetric.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 ).
Reimplemented from umontreal.ssj.discrepancy.Discrepancy.
Definition at line 100 of file DiscL2Symmetric.java.
◆ compute() [3/3]
| double umontreal.ssj.discrepancy.DiscL2Symmetric.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.
Reimplemented from umontreal.ssj.discrepancy.Discrepancy.
Definition at line 57 of file DiscL2Symmetric.java.
The documentation for this class was generated from the following file:
- src/main/java/umontreal/ssj/discrepancy/DiscL2Symmetric.java
