|
SSJ V. labo. |
||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |
java.lang.Objectumontreal.iro.lecuyer.discrepancy.Discrepancy
umontreal.iro.lecuyer.discrepancy.DiscShift1
public class DiscShift1
This class computes the discrepancy for 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),
and the notation {x} means the
fractional part of x, defined here as
{x} = x mod 1.
In one dimension, the formula simplifies to
where zi is the point i.
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
Constructor Summary | |
---|---|
DiscShift1()
Empty constructor. |
|
DiscShift1(double[][] points,
int n,
int s)
Constructor with the n points points[i] in s dimensions and with all weights γr = 1. |
|
DiscShift1(double[][] points,
int n,
int s,
double[] gamma)
Constructor with the n points points[i] in s dimensions, and with the weights γr = gamma[r-1], r = 1,…, s. |
|
DiscShift1(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). |
|
DiscShift1(PointSet set)
Constructor with the point set set. |
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 in dimension s with γr = gamma[r-1]. |
double |
compute(double[] T,
int n)
Computes the discrepancy for the 1-dimensional set of n 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 DiscShift1(double[][] points, int n, int s)
public DiscShift1(double[][] points, int n, int s, double[] gamma)
public DiscShift1(int n, int s, double[] gamma)
public DiscShift1(PointSet set)
public DiscShift1()
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
|
SSJ V. labo. |
||||||||
PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD |