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### SOBOLSEQUENCE

SOBOLSEQUENCE

The SOBOLSEQUENCE function generates numbers from the Sobol sequence. A Sobol sequence is a low discrepancy quasi-random sequence. Sobol sequences were designed to fill space in a more uniform manner than completely random sampling.

The figures below show the differences between a Sobol sequence and sampling uniformly at random.

250 points sampled in 2D with a Sobol sequence.

250 points sampled uniformly in 2D at random.

## Example

### Basic Functionality

`print, SobolSequence(2, 4)`

IDL prints:

`0.50000000      0.50000000`
`0.25000000      0.75000000`
`0.75000000      0.25000000`
`0.37500000      0.62500000`

### Using STATE

`state = 3`
`print, SobolSequence(state, 2)`

IDL prints:

`0.50000000      0.50000000      0.50000000`
`0.25000000      0.75000000      0.25000000`

Print the next two sets of values by using STATE:

`print, SobolSequence(state, 2)`

IDL prints:

`0.75000000      0.25000000      0.75000000`
`0.37500000      0.62500000      0.12500000`

## Syntax

Result = SOBOLSEQUENCE(STATE [, COUNT])

## Return Value

SOBOLSEQUENCE returns an array containing the point(s) in normalized space.

## Arguments

### STATE

A scalar denoting the number of dimensions to use while initializing the state of the Sobol sequence. This value must be in the range of [1, 6].

If STATE is:

• A constant or expression containing a scalar long integer: The value is used to initialize the state of the Sobol sequence.
• A named variable containing a scalar long integer: The value is used to start a new sequence and the resulting state object is returned in STATE.
• A named variable that contains the state from a previous call: It is used to continue the quasi-random sequence, and the resulting state is returned in STATE.

### COUNT

The number of points to return. If omitted, the default is a single n-dimensional point.

None.

## References

SOBOLSEQUENCE is based on the routine sobseq described in section 7.7 of Numerical Recipes in C: The Art of Scientific Computing (Third Edition), published by Cambridge University Press, and is used by permission.

## Version History

 8.7.3 Introduced

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