QuasiRandom
Class NX

java.lang.Object
  QuasiRandom.LowDiscrepancySequence
      QuasiRandom.NX

public class NX

extends LowDiscrepancySequence

Niederreiter-Xing low discrepancy sequence with basis b=2 in dimension at most 20. Uses the Gray code counter and bitwise operations for very fast point generation.

Use N=2^n-1, n=1,2,... points for QMC integration. At N=2^n-1 the Gray code counter G(k) is in sync with the integer sequence k=1,2,... again, that is { G(1),...,G(N) }={ 1,...,N }.

Contains the generator matrices for dimensions j=4...20 in the array gMC decoded from the row encoded form of the download and reencoded column by column for use with the Gray code counter method in the NX point generation.

The columns of the binary matrices are encoded as a decimal integers with the bits in each column forming the digits of the encoding modulo two. The significance of the bits increases bottom up (the top bit is the most significant). This ordering of the bits is necessary for the fast point generation with the Gray code counter.

Field Summary

static int[][][]

gMC gMR.................generator matrix rows.

Constructor Summary

NX(int dim)
NX low discrepancy sequence in dimension dim.

Method Summary

java.lang.String	getName() Name of sequence.
static void	main(java.lang.String[] args) TEST PROGRAM
double[]	nextPoint() The next nx point in the unit cube [0,1]^dim.
void	restart() THE NX POINTS

Methods inherited from class QuasiRandom.LowDiscrepancySequence

L2_discrepancy, L2_discrepancy, nextPoint, nextQuasiNormalVector, projectionPlot

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

gMC

public static final int[][][] gMC

gMR.................generator matrix rows. gMR[j][k] is the kth row of the generator matrix C(j) encoded as a decimal integer n by viewing the the sequence of zeros and ones in the row r_k=row_k(C(j)) as the digits of n in base 2 with the most significant digit being the first component of the row vector r_k. This is the download from the NX sequences site.

Constructor Detail

NX

public NX(int dim)

NX low discrepancy sequence in dimension dim.

Parameters:

dim - dimension of the sequence.

Method Detail

getName

public java.lang.String getName()

Description copied from class: LowDiscrepancySequence

Name of sequence.

Specified by:

getName in class LowDiscrepancySequence

restart

public void restart()

THE NX POINTS

Overrides:

restart in class LowDiscrepancySequence

nextPoint

public double[] nextPoint()

The next nx point in the unit cube [0,1]^dim.

Specified by:

nextPoint in class LowDiscrepancySequence

main

public static void main(java.lang.String[] args)

TEST PROGRAM