chaospy.create_sobol_samples

chaospy.create_sobol_samples(order, dim, seed=1)

Generates samples from the Sobol sequence.

Sobol sequences (also called LP_T sequences or (t, s) sequences in base 2) are an example of quasi-random low-discrepancy sequences. They were first introduced by the Russian mathematician Ilya M. Sobol in 1967.

These sequences use a base of two to form successively finer uniform partitions of the unit interval and then reorder the coordinates in each dimension.

Args:

order (int):

Number of unique samples to generate.

dim (int):

Number of spacial dimensions. Must satisfy 0 < dim < 1111.

seed (int):

Starting seed. Non-positive values are treated as 1. If omitted, consecutive samples are used.

Returns:

(numpy.ndarray):

Quasi-random vector with shape == (dim, order).

Notes:

Implementation based on the initial work of Sobol [1]. This implementation is based on the work of Burkardt.

Examples:

>>> distribution = chaospy.Iid(chaospy.Uniform(0, 1), 2)
>>> samples = distribution.sample(3, rule="sobol")
>>> samples.round(4)
array([[0.5 , 0.75, 0.25],
       [0.5 , 0.25, 0.75]])
>>> samples = distribution.sample(4, rule="sobol")
>>> samples.round(4)
array([[0.5  , 0.75 , 0.25 , 0.375],
       [0.5  , 0.25 , 0.75 , 0.375]])