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SSJ V. labo. |
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java.lang.Objectumontreal.iro.lecuyer.discrepancy.Discrepancy
umontreal.iro.lecuyer.discrepancy.DiscL2Hickernell
public class DiscL2Hickernell
This class computes the Hickernell L2-star discrepancy in for a point set. It is based on the reproducing kernel Hilbert space which consists of functions with square-integrable first-order derivatives, and whose reproducing kernel is given by
.
u⊆S∫[0, 1)|
u|
dx[tex2html_wrap_indisplay273]u,
u|
denotes the cardinality of
[tex2html_wrap_inline279]u,
x[tex2html_wrap_inline281]u denotes the
vector made of the components of
x whose indices are in
[tex2html_wrap_inline284]u,
and
a∈[0, 1]s is called the anchor.
The worst-case error for this function space is the L2 version of the star discrepancy D2*. Choosing [tex2html_wrap_inline294]a = 1, Hickernell obtained the formula
where n is the number of points of set P, s is the dimension of the points, and zik is the k-th coordinate of point i.In 1 dimension, the formula is equivalent to
where zi is the coordinate of point i.
| Constructor Summary | |
|---|---|
DiscL2Hickernell()
Empty constructor. |
|
DiscL2Hickernell(double[][] points,
int n,
int s)
Constructor with the n points points[i] in dimension s. |
|
DiscL2Hickernell(int n,
int s)
Constructor with n points in dimension s. |
|
DiscL2Hickernell(PointSet set)
Constructor with the point set set. |
|
| Method Summary | |
|---|---|
double |
compute(double[][] points,
int n,
int s)
Computes the Hickernell L2-discrepancy for the set of n s-dimensional points points. |
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 Hickernell L2-discrepancy for the set of n 1-dimensional points T. |
| 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 |
|---|
public DiscL2Hickernell(double[][] points,
int n,
int s)
public DiscL2Hickernell(int n,
int s)
public DiscL2Hickernell(PointSet set)
public DiscL2Hickernell()
| Method Detail |
|---|
public double compute(double[][] points,
int n,
int s,
double[] gamma)
Discrepancy
compute in class Discrepancy
public double compute(double[][] points,
int n,
int s)
compute in class Discrepancy
public double compute(double[] T,
int n)
compute in class Discrepancy
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SSJ V. labo. |
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