Statistics Toolbox™

haltonset - Construct Halton quasi-random point set

Class

@haltonset

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.

Example

Generate a 3-dimensional 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

Reference