|
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.DiscShiftBaker1
public class DiscShiftBaker1
DiscShiftBaker1
This class computes the discrepancy for randomly shifted, then baker
folded points of a set P. It is given by[#!vHIC02a!#, eq. 15]
| [D(P)]2 | = | -1 + ![]() ![]() ![]() (1 - [B4({xir - xjr}) - B4({{xir - xjr} -1/2})] |
|
- [7B4({xir - xjr}) - 2B4({{xir - xjr} -1/2})] |
|||
- [B6({xir - xjr}) - B6({{xir - xjr} -1/2})]), |
| [D(P)]2 | = | [tex2html_wrap_indisplay352][tex2html_wrap_indisplay353][tex2html_wrap_indisplay354][- [B4({xi - xj}) - B4({{xi - xj} -1/2})] |
|
- [7B4({xi - xj}) - 2B4({{xi - xj} -1/2})] |
|||
- [B6({xi - xj}) - B6({{xi - xj} -1/2})]]. |
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}) + 
Bα(xr)Bα(yr)],

γu-2γv-2
dxv[![$\displaystyle \htint_{{[0,1]^{S-v}}}^{}$](DiscShiftBaker1img17.png)
dxS-v]2,
γr.
| Constructor Summary | |
|---|---|
DiscShiftBaker1()
. |
|
DiscShiftBaker1(double[][] points,
int n,
int s)
. |
|
DiscShiftBaker1(double[][] points,
int n,
int s,
double[] gamma)
. |
|
DiscShiftBaker1(int n,
int s,
double[] gamma)
. |
|
DiscShiftBaker1(PointSet set)
. |
|
| Method Summary | |
|---|---|
double |
compute(double[][] points,
int n,
int s)
. |
double |
compute(double[][] points,
int n,
int s,
double[] gamma)
. |
double |
compute(double[] T,
int n)
. |
double |
compute(double[] T,
int n,
double 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 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 |
|---|
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
|
SSJ V. labo. |
||||||||
| PREV CLASS NEXT CLASS | FRAMES NO FRAMES | ||||||||
| SUMMARY: NESTED | FIELD | CONSTR | METHOD | DETAIL: FIELD | CONSTR | METHOD | ||||||||