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SSJ V. labo. |
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java.lang.Objectumontreal.iro.lecuyer.discrepancy.Discrepancy
umontreal.iro.lecuyer.discrepancy.DiscShiftBaker1
public class DiscShiftBaker1
This class computes the discrepancy for randomly shifted, then baker
folded points of a set P. It is given by
[D(P)]2 | = | -1 + ![]() ![]() |
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bernoulliPoly
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
[D(P)]2 | = | [tex2html_wrap_indisplay349]∑i=1n∑j=1n[- ![]() |
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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 | |
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DiscShiftBaker1()
Empty constructor. |
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DiscShiftBaker1(double[][] points,
int n,
int s)
Constructor with the n points points[i] in s dimensions, with all the weights γr = 1. |
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DiscShiftBaker1(double[][] points,
int n,
int s,
double[] gamma)
Constructor with the n points points[i] in s dimensions, with weights γr = gamma[r-1]. |
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DiscShiftBaker1(int n,
int s,
double[] gamma)
The number of points is n, the dimension s, and the s weight factors are gamma[r], r = 0, 1,…,(s - 1). |
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DiscShiftBaker1(PointSet set)
Constructor with the point set set. |
Method Summary | |
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double |
compute(double[][] points,
int n,
int s)
Computes the discrepancy for the s-dimensional points of set points, containing n points. |
double |
compute(double[][] points,
int n,
int s,
double[] gamma)
Computes the discrepancy for the first n points of 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 |
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compute, compute, compute, compute, compute, compute, formatPoints, getDimension, getGamma, getName, getNumPoints, setGamma, setPoints, setPoints, sort, toArray, toString |
Methods inherited from class java.lang.Object |
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equals, getClass, hashCode, notify, notifyAll, wait, wait, wait |
Constructor Detail |
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public DiscShiftBaker1(double[][] points, int n, int s)
public DiscShiftBaker1(double[][] points, int n, int s, double[] gamma)
public DiscShiftBaker1(int n, int s, double[] gamma)
public DiscShiftBaker1(PointSet set)
public DiscShiftBaker1()
Method Detail |
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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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