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haltonset

Class: haltonset

Construct Halton quasi-random point set

Syntax

p = haltonset(d)
p = haltonset(d,prop1,val1,prop2,val2,...)

Description

p = haltonset(d) constructs a d-dimensional point set p of the haltonset class, with default property settings.

p = haltonset(d,prop1,val1,prop2,val2,...) specifies property name/value pairs used to construct p.

The object p returned by haltonset encapsulates properties of a specified quasi-random sequence. The point set is finite, with a length determined by the Skip and Leap properties and by limits on the size of point set indices (maximum value of 253). Values of the point set are not generated and stored in memory until you access p using net or parenthesis indexing.

Examples

Generate a 3-D Halton point set, skip the first 1000 values, and then retain every 101st point:

p = haltonset(3,'Skip',1e3,'Leap',1e2)
p = 
    Halton point set in 3 dimensions (8.918019e+013 points)
    Properties:
              Skip : 1000
              Leap : 100
    ScrambleMethod : none

Use scramble to apply reverse-radix scrambling:

p = scramble(p,'RR2')
p = 
    Halton point set in 3 dimensions (8.918019e+013 points)
    Properties:
              Skip : 1000
              Leap : 100
    ScrambleMethod : RR2

Use net to generate the first four points:

X0 = net(p,4)
X0 =
    0.0928    0.6950    0.0029
    0.6958    0.2958    0.8269
    0.3013    0.6497    0.4141
    0.9087    0.7883    0.2166

Use parenthesis indexing to generate every third point, up to the 11th point:

X = p(1:3:11,:)
X =
    0.0928    0.6950    0.0029
    0.9087    0.7883    0.2166
    0.3843    0.9840    0.9878
    0.6831    0.7357    0.7923

References

[1] Kocis, L., and W. J. Whiten. "Computational Investigations of Low-Discrepancy Sequences." ACM Transactions on Mathematical Software. Vol. 23, No. 2, 1997, pp. 266–294.

See Also

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