sobolset

Class: sobolset

Construct Sobol quasi-random point set

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.

Examples

Generate a 3-D 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, 1988, pp. 88–100.

[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, 2003, pp. 49–57.

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

[4] Matousek, J. "On the L2-Discrepancy for Anchored Boxes." Journal of Complexity. Vol. 14, No. 4, 1998, pp. 527–556.

See Also

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