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SSJ V. labo. |
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java.lang.Objectumontreal.iro.lecuyer.discrepancy.Discrepancy
umontreal.iro.lecuyer.discrepancy.DiscShift2
public class DiscShift2
This class computes the discrepancy in for the randomly shifted points of a set P. It is given by
where n is the number of points of P, s is the dimension of the points, xir is the r-th coordinate of point i, and the γr are arbitrary positive weights. The Bα(x) are the Bernoulli polynomials of degree α (seebernoulliPoly
in class util/Num). The notation {x} means the
fractional part of x, defined as
{x} = x mod 1.
In one dimension, the formula simplifies to
The discrepancy represents a worst-case error criterion for the approximation of integrals, when the integrands have a certain degree of smoothness and lie in a Hilbert space H with a reproducing kernel K given by
B4({xr - yr}) + ∑α=02
Bα(xr)Bα(yr)],
dxS-v]2,
| Constructor Summary | |
|---|---|
DiscShift2()
Empty constructor. |
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DiscShift2(double[][] points,
int n,
int s)
Constructor with the n points Pi = points[i] in dimension s, with all weights γj = 1. |
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DiscShift2(double[][] points,
int n,
int s,
double[] gamma)
Constructor with the n points Pi = points[i] in dimension s, with the weights γj = gamma[j-1], j = 1,…, s. |
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DiscShift2(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). |
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DiscShift2(PointSet set)
Constructor with the point set set. |
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| Method Summary | |
|---|---|
double |
compute(double[][] points,
int n,
int s)
Computes the discrepancy for the first n points of set points in dimension s. |
double |
compute(double[][] points,
int n,
int s,
double[] gamma)
Computes the discrepancy for the first n points of set points in dimension s and with weight γr = gamma[r-1]. |
double |
compute(double[] T,
int n)
Computes the discrepancy for the first n points of T in 1 dimension, with weight γ = 1. |
double |
compute(double[] T,
int n,
double gamma)
Computes the discrepancy for the first n points of T in 1 dimension, with weight γ = gamma. |
| Methods inherited from class umontreal.iro.lecuyer.discrepancy.Discrepancy |
|---|
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 DiscShift2(double[][] points,
int n,
int s)
public DiscShift2(double[][] points,
int n,
int s,
double[] gamma)
public DiscShift2(int n,
int s,
double[] gamma)
public DiscShift2(PointSet set)
public DiscShift2()
| Method Detail |
|---|
public double compute(double[][] points,
int n,
int s)
compute in class Discrepancy
public double compute(double[][] points,
int n,
int s,
double[] gamma)
compute in class Discrepancy
public double compute(double[] T,
int n)
compute in class Discrepancy
public double compute(double[] T,
int n,
double gamma)
compute in class Discrepancy
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SSJ V. labo. |
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| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD | ||||||||