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java.lang.Object umontreal.iro.lecuyer.hups.PointSet umontreal.iro.lecuyer.hups.DigitalNet umontreal.iro.lecuyer.hups.DigitalNetBase2 umontreal.iro.lecuyer.hups.DigitalSequenceBase2 umontreal.iro.lecuyer.hups.SobolSequence
public class SobolSequence
This class implements digital nets or digital sequences in base 2 formed by the first n = 2^{k} points of a Sobol' sequence. Values of n up to 2^{30} are allowed.
In Sobol's proposal, the generator matrices C_{j} are upper triangular matrices defined by a set of direction numbers
For each dimension j, the integers m_{j, c} are defined by selecting a primitive polynomial over F_{2} of degree c_{j},
This list of primitive polynomials, as well as default choices for the direction numbers, are stored in precomputed tables. The ordered list of primitive polynomials was taken from Florent Chabaud's web site, at http://fchabaud.free.fr/. Each polynomial f_{j}(z) is stored in the form of the integer 2^{cj} + a_{j, 1}2^{cj1} + ^{ ... } + a_{j, cj}, whose binary representation gives the polynomial coefficients.
For the set of direction numbers, there are several possibilities based on different selection criteria. The original values proposed by Sobol' and implemented in the code of Bratley and Fox for j <= 40 were selected in terms of his properties A and A', which are equivalent to sdistribution with one and two bits of accuracy, respectively. The default direction numbers used here have been taken from Lemieux et al. For j <= 40, they are the same as in Bratley and Fox. Several files of parameters for Sobol sequences are given on F. Kuo's Web site at http://web.maths.unsw.edu.au/~fkuo/sobol/index.html.
Constructor Summary  

SobolSequence(int n,
int dim)
Constructs a Sobol point set with at least n points and 31 output digits, in dimension dim. 

SobolSequence(int k,
int w,
int dim)
Constructs a new digital net with n = 2^{k} points and w output digits, in dimension dim, formed by taking the first n points of the Sobol' sequence. 

SobolSequence(String filename,
int k,
int w,
int dim)
Constructs a new digital net using the direction numbers provided in file filename. 
Method Summary  

void 
extendSequence(int k)
Increases the number of points to n = 2^{k} from now on. 
String 
toString()
Formats a string that contains information about the point set. 
Methods inherited from class umontreal.iro.lecuyer.hups.DigitalSequenceBase2 

iteratorShift, iteratorShiftNoGray, toNet, toNetShiftCj 
Methods inherited from class umontreal.iro.lecuyer.hups.DigitalNet 

eraseOriginalGeneratorMatrices, resetGeneratorMatrices, unrandomize 
Methods inherited from class umontreal.iro.lecuyer.hups.PointSet 

addRandomShift, addRandomShift, formatPoints, formatPoints, formatPoints, formatPoints, formatPointsBase, formatPointsBase, formatPointsBase, formatPointsBase, formatPointsNumbered, formatPointsNumbered, getDimension, getNumPoints, getStream, randomize, randomize, randomize, randomize, randomize, setStream 
Methods inherited from class java.lang.Object 

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait 
Constructor Detail 

public SobolSequence(int k, int w, int dim)
k
 there will be 2^k pointsw
 number of output digitsdim
 dimension of the point setpublic SobolSequence(int n, int dim)
dim
 dimension of the point setn
 minimal number of pointspublic SobolSequence(String filename, int k, int w, int dim)
net = new SobolSequence(
"http://web.maths.unsw.edu.au/˜fkuo/sobol/joekuo6.16900", k, w, dim);
The file must have the following format (the first line is treated as a comment by the program and discarded):
dim  s  a  m_{i} 
2  1  0  1 
3  2  1  1 3 
4  3  1  1 3 1 
5  3  2  1 1 1 
6  4  1  1 1 3 3 
7  4  4  1 3 5 13 
⋮  ⋮ 
k
 number of points is 2^{k}w
 number of output digitsdim
 dimension of the point setfilename
 file containing the direction numbersMethod Detail 

public String toString()
PointSet
toString
in class DigitalNetBase2
public void extendSequence(int k)
DigitalSequenceBase2
extendSequence
in class DigitalSequenceBase2
k
 there will be 2^k points

SSJ V. 2.6. 

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