Statistics Toolbox™

sobolset - Construct Sobol quasi-random point set

Class

@sobolset

Syntax

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

Description

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

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

The object p returned by sobolset 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 Sobol point set, skip the first 1000 values, and then retain every 101st point:

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

Use scramble to apply a random linear scramble combined with a random digital shift:

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

Use net to generate the first four points:

X0 = net(p,4)
X0 =
    0.7601    0.5919    0.9529
    0.1795    0.0856    0.0491
    0.5488    0.0785    0.8483
    0.3882    0.8771    0.8755

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

X = p(1:3:11,:)
X =
    0.7601    0.5919    0.9529
    0.3882    0.8771    0.8755
    0.6905    0.4951    0.8464
    0.1955    0.5679    0.3192

References

[1] Bratley, P., and B. L. Fox, "ALGORITHM 659: Implementing Sobol's Quasirandom Sequence Generator," ACM Transactions on Mathematical Software, Vol. 14, No. 1, pp. 88-100, 1988.

[2] Joe, S., and F. Y. Kuo, "Remark on Algorithm 659: Implementing Sobol's Quasirandom Sequence Generator," ACM Transactions on Mathematical Software, Vol. 29, No. 1, pp. 49-57, 2003.

[3] Hong, H. S., and F. J. Hickernell, "ALGORITHM 823: Implementing Scrambled Digital Sequences," ACM Transactions on Mathematical Software, Vol. 29, No. 2, pp. 95-109, 2003.