# Documentation

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# 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.